Not exactly a prediction, but a possible scenario. Following the passage of the Fiscal Cliff deal by a Democratic/Republican coalition, John Beohner is challanged for Speaker of the House. He gets a majority of the Republican caucus, but the Tea Partiers refuse to go along and support him on the floor.
Beohnor approaches Pelosi and they make a deal. Democrats will support Beohner for speaker. The price is that he will allow the Democrats to bring bills to the floor. Real business starts to happen in the committees and on the floor. Most bills are passed by some combination of Democratic and Republican votes. The Tea Partiers are sidelined and government goes on without them.
Remember when party line votes were uncommon? Bills went through committees and ammendments were offered and voted up or down. In the end a member had to decide if the final result was worth supporting or not. You had to win over a majority of the House, not a majority of the majority party. It was messy and far from perfect, but it was democracy.