Why do u.s. politicians obsess over helping the middle class?

It's important to note that to an American, they're middle class almost completely irrespective of their circumstances. Single parent living in subsidized housing, working for near minimum wage? Middle class. Lower middle class, maybe, if we're not feeling defensive. McMansion, dual income family with one doctor and one lawyer? Driving expensive European cars (one for each adult, plus one for the teenager), vacationing abroad yearly, middle class, maybe, maybe, upper middle class if they're feeling embarrassed about their wealth.
Your family owns the only plumbing company in town and you have several houses a small fleet of vehicles and dozens of employees. Your surname is a local household name. The highschool gym is named after your grandpa. Sure you're prosperous but upper class? Idk, I mean listen you have to go to work, sometimes, at the sinecure your dad got you at said plumbing company. Real rich people don't have to pretend to work, right?
Everyone pretends to be middle class.

To add to the other comments here, the middle class doesn't really exist. So when you promise to help the middle class, you're promising to help no one.
There are clearly defined classes with clearly defined and antagonistic interests, so the mythical middle class is a way for the bourgeoisie to hide the fact that they have no interest in serving the working class by claiming to serve an "average" class that doesn't exist and seems to in practice have the same interests as the bourgeoisie.
The "piss on my head and tell me it's raining" of the American political jargon.
- Yup I came here to say basically this. The middle class is a scapegoat that reinforces the idea that you're a moral and abject failure for not rising to this gilded position within American society. Solving the issues of the underclass undermines the entire middle-class mythos and would cause a self reinforcing reaction from those who think they are in that class. By giving the underclass more you create the perception that you're not helping the middle class. Forget rising tides lifting all boats.

random stat i half remember from
is something that like 80% of Americans consider themselves to be "middle class". When politicians say "middle class", they can appeal to basically everyone while the average listener feels like they're being spoken to more specifically
- TBF, that probably tallies quite will with the labour aristocracy numbers.

The "middle class" is an extremely nebulous class of people mostly defined by vibes, and since most people don't want to identify as outright poor, they like to identify as middle class since it's basically open to anybody due to how vague it is.
Poor people will call themselves middle class (maybe qualify it as "lower middle class"), wealthy people will call themselves middle class (maybe qualify it as "upper middle class"), and so politicians can make hollow but safe appeals to this nebulous class that tons of people identify as, but which nobody really coherently belongs too.
So basically, "I will help the middle class" is speaking to no-one, because the middle class doesn't really exist, but people will hear it and think you're speaking to them.
- this. it's a rhetorical tool that misidentifies the interests of the working class with those of the owning class.
  
  ...with the goal of suppressing class consciousness, and dividing workers. The same is true of anti-immigration rhetoric, sexism, and racism. "See that 'other' kind of person over there? They want what's yours." It all distracts from the capitalists robbing us blind.

because 99% of poor people identify themselves as middle class because they don't want to be "the poor"
- And rich people know the "middle class" is a hoax to dupe poor into supporting policies aimed against the poor.
  
  exactly
- 99% of rich people also classify themselves as middle or upper-middle fwiw.

It has a lot to do with the concepts of "The American Dream" & "Equality of Opportunity" being poor is seen ultimately as being a personal/moral failure and all poor people instead of demanding change should instead keep quiet and buckle down and maybe if they work hard enough they will be able to send their kid to college so they can join the mythical middle class and live a cushy middle class lifestyle with a house in the suburbs with a white picket fence, 2.5 kids and a dog etc.

Because the "middle class" is a fictitious category that everyone from people struggling to stay above the poverty line to literal millionaires think they belong to. It's what "respectable" people are, the small landholders and people who aspire to own land.
It was cynically created by encouraging suburban land ownership among certain privileged (white) working class demographics, and later reinforced by encouraging tying small amounts of stock ownership into pensions or workers' benefits. It's a way of making workers mistakenly see their own material interests as being aligned with the ruling class's, and insulating them against reforms that would benefit them directly at the cost of meaning less value for the meager property they've acquired.

Citation Needed Episode 91: It's Time to Retire the Term "Middle Class"
The term “middle class” is used so much by pundits and politicians, it could easily be the Free Space in any political rhetoric Bingo card. After all, who’s opposed to strengthening, widening, and protecting the “middle class”? Like “democracy,” “freedom,” and “human rights”, “middle class” is an unimpeachable, unassailable label that evokes warm feelings and a sense of collective morality.
But the term itself, always slippery and changing based on context, has evolved from a vague aspiration marked by safety, a nice home, and a white picket fence into something more sinister, racially-coded, and deliberately obscuring. The middle class isn’t about concrete, material positive rights of good housing and economic security––it’s a capitalist carrot hovering over our heads telling us such things are possible if we Only Work Harder. More than anything, it's a way for politicians to gesture towards populism without the messiness of mentioning––much less centering––the poor and poverty.

You have to remember the puritanical roots of the country.
The upper/middle/lower class distinctions are not economic:
upper = rich;
middle = comfortable;
lower = poor.
They're instead based on morality:
upper = blessed;
middle = virtuous strivers;
lower = good-for-nothing work-shy losers.
The upper class have been divinely marked for better things. They are never helped. Everything they receive is ordained. The lower class are scum who it would be wrong to ever help, since it would only encourage their inherent unwillingness to work. The middle class, then, are the self-made people who work hard for what they get and obviously deserve a little more, which in self-image terms is basically everyone.
Politicians promising to help the middle class are, therefore, declaring that they will reward the worthy (and punish the unworthy), which is a popular sentiment.

because americans are the most propagandized people in the history of planet earth.

everyone thinks they're "middle class". even people who know for a fact they're poor as hell will also identify themselves as "middle class" and then people who are super well off are clueless to the suffering of the real world so they also assume they're "middle class" because they don't interact with poor people and then out of their 10 friends their family is only the 6th richest

One thing I've heard from Americans is that what everyone else calls 'working class' they call 'middle class'. This is probably due to a hope that one day they will 'make it big', and a reluctance to see themselves as 'below average'.
- one thing i've noticed in british political discourse is that "middle class" is still used, but it emphatically does not include the working masses. my sense is that it encapsulates professionals and petty bourgeoisie, as well as having more rigid cultural identity connotations? and then "upper class" is like, multimillionaires and people with titles? someone tells me if i'm off here.
  
  This is correct. 'Middle class' is more or less 'people who need to work for a living, but can work on their terms'. Petty bourgeoisie, professionals, people who see themselves as 'respectable' and 'above the riff-raff'.

Because it’s vague as a concept so their messaging can also be vague

It has a lot to do with the idea that there is socio-economic mobility in the US if they work hard enough. Add to that the fact that many people see themselves as middle class rather than lower class even though the vast majority of the US is closer, if not already, lower class.

To add to everything else that's been said here it's the only "class" that politicians can talk about safely. Talk about helping the lower class and you're a dreaded commie. Talk about helping the upper class and you're one of those dreaded elites.

Because middle class is a dog whistle for white and working class is a dog whistle for black/brown. Except lots of black and brown people who live comfortable lives think politicians are talking about them.

There's a long answer and basically it's my thesis that as Jim Crow was obviously untenable long-term, the powers that be set about transposing the American apartheid model onto the economic sphere so that way it becomes diffuse and mystified; there's no clear way to dismantle the system or to petition it for redress and so on (well, I can think of one way...)
Basically the middle class in America is a pseudo-caste that exists because of the economic conditions that caused it to flourish by design.
Here's my hot take on this whole deal
There's other stuff to be discussed on thw topic of your question about how this shapes and structures aspiration, how it obscures the realities of class warfare, and how strictly limits the scope of what's acceptable within bourgeois democracy etc. etc. that I'm sure other comrades have answered better than I could.

The "middle class" is a quite successful attempt by bourgeois propaganda to create a new socioeconomic analysis that is not rooted in the actual objective role we have in our economy, as in workers who produce vs capitalists who own the means of production, but in a subjective metamodernist perspective where everyone is the same in the economic system and seperated simply by the money they make. People who are quite rich by owning land can still be considered middle class, while someone who works a white collar job like software engineering is also considered middle class despite the huge difference in systemic role. The fact that the "middle class" landowner is rich through exploitation is neatly tucked away in a layer of capitalist utopia where everyone can also become a capitalist if they simply try very hard, and no harm will be done by you doing that.
One goal of this is to hide away and try to make Marxism forgotten and left in the past, because it is the only true socioeconomic analysis that truly explains our reality and highlights the clear class distinctions that are inherent to capitalism which it can't exist without. Only Marxism really shows the contradictions in the root of capitalism, the constant clash between the proletariat which produces everything and keeps getting more and more able to do so collectively with a common goal, and the bourgeoisie who privately own the means of production and capital in general and force the proletariat to work for them by giving them a small part of the value they create. The latter keeps becoming a smaller and smaller class that is constantly getting more disconnected with the actual production process, at the same time that the former is becoming more collective than ever and has the potential to break away and self organize to produce with the goal of giving straight to the people according to their needs instead of the capitalist's antagonistic goals.
Another goal is to perpetuate the delusion that lower working class people who don't belong to the beloved middle class, can grit their teeth and work hard enough to get there, while the rest can enjoy their position within it and rightfully ignore the suffering of the lower class since they worked for and therefore deserve their privileges.

Case in point to what everyone else is saying.
I carpooled at a previous job with two people.
One of them was from a stable established family that owned a nice house swimming pool, land, vehicles, and equipment, and he could have inherited the successful family business with government contracts on the order of a million dollars if he wanted to, in addition to the extensive stock portfolio he'd been set up with. The other was raised by a single mom in a trailer as 1 of 6 children, and never had so much as a career path.
Both of these guys adamantly claimed that they were middle class- the first because he was making about the median income for the area, the second because he and his ex had once had a combined income of over $100,000.

the bourgeoisie (bourg=city/market town, compare burg/berg) were the middle class in the feudal system, not serfs or peasants, not clergy or lords, they were the craftspeople and merchants that lived in cities.
this same middle class is the ruling class of bourgeois nations like the united states. US politicians are most enthusiastic about helping themselves. and this is laundered to portions of the working class who imagine themselves part of that class, through the characteristics of the 'middle class': unlike nobility which comes with a title, the bourgeoisie do not have a prescribed job title or an authority that they derive legitimacy from. they can be moneychangers, rentiers, industrialists, independent craftspeople (petit-bourgeoisie), successful professionals that parlay accumulated wealth into property, etc---it's fucking complicated---and it is unstable. if and when the wealth and property is stripped of an individual or family, they no longer belong to the class. So it is very easy for people experiencing more comfort than the poorest parts of society to imagine themselves as part of such an encompassing and flexible class. Own a house (something a literal peasant could, then renting the fields from the lord)? middle class. Own penny stocks? middle class. Literally just think you're wealthier than your poorest neighbor? middle class.

There is no middle class. But most working class people consider themselves to be middle class. So politicians use it as an easy go to.
There is only working class and ruling class. Everything else is just flash.

They fight on behalf of the middle class because they are a part of it. The problem is that they're using the original definition of the middle class which meant the class between the aristocracy and the peasantry.

False hope of a bygone age. Deflect from the oligarchs keeping the working poor down and developing class concioisness. The myth of the
American Dream and the nuclear family. As long as there is hope and enough bullshit to weasel people into thinking someday they'll own a modest $400k "starter home".
- I found a YouTube link in your comment. Here are links to the same video on alternative frontends that protect your privacy:
  yewtu.be
  inv.nadeko.net
  yt.artemislena.eu
  piped.video

the people not marked dregs, because of their lack of power; the people they know have different needs and interests and are easily bought, who have sufficient wealth to be a Problem and should be placated until their power can be removed entirely, which is in-progress right now, but for now a shrinking cohort of enablers of empire who will soon be as debt shackled and landless as the people they leave behind, having taken their bribe.