I find that the opposite is true. Poor people tend to lean left. It's just that conservatives don't take care of their impoverished populations, so the whole area rots economically from the bottom up.
One example that hits particularly close to my home is how republicans are vehemently against raising the minimum wage. But they also can't figure out why fast food joints and grocery stores around here can't keep enough staff to stay open.
Nobody can afford to live on 7.25/hr anymore. But republicans here will never acknowledge that. So our economy suffers.
Au contraire - poverty drives people to the left, historically.
There are other factors at play here, covered by others in great detail; the most important being that rural areas (that are obviously poorer than business centers) are more conservative, and with that, Republican.
Poverty drives people to political disaffection. Low-Income voters are the least likely to vote. Less than 30% describe themselves as liberal or somewhat liberal.