The following are speculations, not predictions:
If they get control of Congress the GOP will try and mostly succeed in enlisting the Tea Party movement in confrontations with President Obama. Among other things, they will hold noisy hearings on red-meat hot-button issues, but will be extremely cautious and selective about holding actual accountability-generating roll call votes on them. Expect no roll call votes on systemic-change issues that challenge the political class itself (like repealing McCain-Feingold's restrictions on political speech, for example, or imposing term limits).
As in 1995, the budget will generate an unavoidable confrontation between a GOP Congress and the administration. We could see a Stalingrad-magnitude conflict, or perhaps GOP members will become puppydogs (and earmark hounds) who roll over to avoid the controversy. Either way, this could administer a huge Tea Party booster shot.
Gridlock will limit new spending programs, but also means no real change to policies already in place (i.e. Obamacare), which will cause tremendous Tea Party frustration and anger. They will try, but will Republicans succeed in channeling all of that against Democrats and Obama?
Republican members and caucuses inevitably will do some foolish, cynical and faithless things that will let President Obama make them the issue in 2012, just as President Clinton did in 1996.
Among other things, this creates the potential for a Perot-type third candidate in 2012 - and an Obama second term.
Republicans may try to ride the tiger of Tea Party anger against the generic, bipartisan political class, betting that Obama and the Democrats get the brunt of it. Will the Tea Party movement be so inflamed by the passion of current battles as to forget that their real beef is with the bipartisan political careerist class as a whole?
At the state level, Republicans will do the minimum systemic reform needed to enable their members to posture as change agents and build "the rest are bums but my guy is alright" immunity for individual members from Tea Party ire. State Republicans will benefit from the national GOP Congress vs. President Obama dynamic if this is primarily characterized by epic battles over issues they care about.
Conclusions: None. Uncertainties abound, and surprises may be the rule.
The following passage from Angelo Codevilla's recent article, America's Ruling Class -- And the Perils of Revolution, provides a larger context for all this; by "country class" he means everyone not in the ruling class, and right now the Tea Party movement is its most visible expression:
Because, in the long run, the country class will not support a party as conflicted as today's Republicans, those Republican politicians who really want to represent it will either reform the party in an unmistakable manner, or start a new one as Whigs like Abraham Lincoln started the Republican Party in the 1850s.
The name of the party that will represent America's country class is far less important than what, precisely, it represents and how it goes about representing it because, for the foreseeable future, American politics will consist of confrontation between what we might call the Country Party and the ruling class.