There actually is a chance that an idea like this could get through Congress, because it's for everyone, not just for people who really need it. Therefore, there's no need to distinguish between the "makers and takers" (to use their parlance). I don't see it being a strong possibility, given that their main strategy is to oppose and not to govern, but ideologically, I think that conservatives should be able to get behind this idea.
You identified the problem clearly. Where they may have some ideological affinity for something like this, they have zero strategic affinity. If something like this would actually be an effective shot in the arm to the economy, they will be opposed to it under a Democratic administration if the President supports it. Conservatives should have been able to get behind the Individual Mandate in the health care bill because it was their idea, proposed by the Heritage Foundation no less. It came from the belly of the Heritage Foundation and ended up with literally 100% opposition by Conservatives and Republicans under Obama's Presidency. Not only was the opposition 100%, but they actually howled and hoisted it up as one of the main proofs of Obama's Socialism. Their idea.I don't see it being a strong possibility, given that their main strategy is to oppose and not to govern, but ideologically, I think that conservatives should be able to get behind this idea.
I wonder if Obama had known then what he knows now (namely, that GOP would oppose anything, no matter how conservative it is, in principle), if he would have pursued a different strategy. In their attempts to compromise, we basically got a terrible law that isn't going to help people nearly as much as it might have. Although there were some democrats who needed quite a bit of convincing, too.