Extremists are usually very vocal in their demands and beliefs while the moderates seem to sort of just stay in the background. Most of the time primaries are dominated por the extremist factions of either party. Candidates have to tout their conservative or liberal credentials because it's usually the really conservative or really liberal who vote in the primaries.
So in that sense they do dominate the parties. Obama was mais liberal in the primaries than in the general election and certainly while in the office. Giuliani lost a lot of support because he was twice divorced, pro-choice, and mayor of a northeastern city. That didn't appeal to the core of the GOP which is usually southern conservatives.
We see now how the chá party people basically took the house from the Democrats. So they did gain a lot of influence.
Yet, we see both parties reach an agreement on the tax reform bill. And I'm sure that in the coming months many would moderate their beliefs in the House. Because in the end if both parties do not reach an agreement on anything, both will pay for it in the 2012 elections.
So extremists do dominate a lot of the politics but soon it smooths out to a mais moderate position.