That would work for them IF they hadn't spent the last eight years saying the GOP was the "party of NO." If they now become the party of no, the Republicans will use that very effectively against them.
I don't think so. There's a double standard where such things are concerned. For the Dems, it can and probably will be characterized as a "principled stand."
The Democrats can, as they always do, claim to be standing up for the little guy -- and they have no scruples about using that endless supply of good folks who really are hurting.
The Republicans, meanwhile, are forced to argue on the basis of why Congress shouldn' help out people who are hurting.
Americans are, by and large, nice people who don't mind helping other people out. And it's very true that good people are hurting. And for that reason, the Democrats have by far the easier job in convincing people of their position.
Over decades they've figured out how to make the emotional appeal, and they've dulled peoples' senses about the economic and moral difficulties associated with their position.
The R's have got to start working on educating people about reality. It may not be possible until things break for real, though.