Traditionally, a failure by the government would result in a gain by the opposition party. However, the peculiar dynamics of the two party system in the US works against this. The two parties have converged into a single dominant party with roughly similar agendas. Further, these parties have rigged the system to prevent third party formation. As a result, there isn't a structured process to absorb this movement into the political system.Robb sketches out some possible repercussions, none of which are solidly positive for Republicans.
I generally agree with this assessment, although clearly Republicans are trying to use the Tea Party to short-term advantage. It's not like Republicans are solid fiscal conservatives either. Ideologically, there's a mismatch, but the mismatch is much stronger at the level of organization. The networked character of the Tea Party, as Robb suggests, is very interesting, more interesting to me than the specific politics.
Last August, I wrote about the related protests at the health care town halls, using Castells, Arquilla and Ronfeldt, and others to theorize the movement's organization and to tie it into previous protests from other ideological quarters. See that post for more on how the movement appears to be organized. And if you're looking for a dissertation topic, I can't think of one that is more fascinating or timely.