Today's USA Today has an article (or maybe it was CNN, I forget) that says that 133 House Republicans would support a straight-up vote on the budget and would pass it. That means to me that the Tea Party members have an outsized impact on the House due in part to their control over Boehner. Moreover, the same number was said to have voted against the piece-meal funding that the Tea Partiers were trying to advance in order to get only the parts of the Government funded that they approve of or are afraid to be seen as blocking. That again says that the majority of the Republicans in the House are at least sane enough to try to to govern rather than obstruct.
The fact that we are still at an impasse tells me though that the Tea Party's outsized influence remains. So many other Republicans (including the Speaker) would be willing to pass a clean bill and let the government function, but for their fear that the Tea Party will run against them in their next primary. So, there are the Tea Partiers and then there are the Republicans who are afraid of the Tea Party. Same difference in practical terms.