If any given state could make a go of it on their own it's CA. Take that away from the USA and there would be some major shifts in the world economic policy. Why anyone would suggest such is a far fetched idea though.
Eh, don't inflate yourself that much. CA is important but it's still dwarfed by the country as a whole. Losing somewhere around 10% of the GDP and population would suck, but it's not the solitary pillar holding things up either.
I think the US is precarious enough that the loss of CA would make the US economy unrecoverable. I think the East Coast would also immediately secede, since without CA the country is in a state of permanent Republican rule. Chicago and Detroit would probably petition to join Canada. I think loss of California would be a blow the US could not recover from as a nation.