The procedure to oust the speaker gets to the floor as a privileged motion. It takes one member to put it on the calendar, and there’s really no way of stopping the motion if the votes are there to support it. Boehner, to stay as speaker, would need the support of a majority of all members present and voting.
Why would any honest Republican support such a move and risk being branded a traitor, a RINO (Republican in Name Only), or worst of all, an Obama-enabler? Recent primary elections have seen tea party candidates defeat incumbent Republicans deemed not conservative enough.
But the favorability of tea party candidates in the eyes of the electorate may be shifting. We’ve seen examples of this at the state level, in Michigan for example.
And state-level budget crises have forced radical bipartisanship, which voters have rewarded. Look at what happened in the Senate in Washington State not too long ago. Three Democrats walked across the aisle, and worked with minority Republicans to craft a compromise budget, breaking a months-long deadlock. The anger of the Democratic leadership and base was fierce. But the state benefited. And voters and editorial boards around the state sang the legislature’s praises.