We're waiting for Eric Cantor to do the right thing and demand tax cuts if people in his own district are going to see any federal money

This is a big problem. The budget is already stretched very thin, and even Cantor has asked his members not to provoke another fight about cutting spending beyond its already agreed-upon levels. And if clean-up costs reach into the billions, paying for it by cutting spending will damage other important services, despite the fact that the usual standard is to not use natural disasters as political bargaining chips.
Three things are going on here by my count. First, Republicans have learned an obvious lesson since they retook the House -- that they can control the agenda in Washington, and put popular government programs under attack, if and only if they have some leverage over Democrats to play along. The government shutdown fight in April was their first victory. The debt limit showdown was their piece de resistance.
Second, there are political pitfalls to this approach, particularly when it requires Republicans to publicly stake out specific positions. Cutting government spending might focus group well, but privatizing Medicare does not, as Republicans learned quite painfully earlier this year. This augurs for slashing spending in nebulous ways -- capping discretionary spending, and spreading the cuts out across myriad federal programs; or promising to "find monies" in the budget to offset new expenses. Death by a thousand, invisible cuts.
Third, the right flank of the Republican party expects no less. In 2005, after Hurricane Katrina devastated southern Louisiana, Cantor's predecessor, Rep. Tom DeLay (R-TX) claimed Republicans had pared discretionary spending back enough that federal aid could be financed with new debt. He came under attack from members of his own party and quickly reversed himself. Looks like Cantor learned his lesson.
But it's a difficult line to walk. Part of what made Republican victories in the shutdown and debt limit fights plausible was a logical veneer that doesn't exist here. "We spend too much money on government programs," Republicans basically argued, "so we won't fund the government unless we impose discipline." Another line was, in effect: "The national debt has skyrocketed, so we won't allow the government to incur more of it unless steps are taken to hold down its growth." When you drilled into these arguments, they crumbled, but at a glance they were quite plausible.
That's not the case after a natural disaster. And if there's a loud cry for federal aid once the damage is assessed, Cantor's position will probably prove unsustainable.

Rest of story here:  http://tpmdc.talkingpointsmemo.com/2011/08/why-republicans-might-demand-hurricane-relief-be-paid-for-with-more-program-cuts.php?ref=fpb