If Republicans hope to salvage what's left of their credibility and legitimacy, then the members of the party are going to have to take bold steps. Often times Republicans these days are characterized by their very loud red-neck cousins who have about as much good sense as a long-tailed cat who lives in a store full of rocking chairs. However, I know for a fact that there are well-meaining truly educated Republicans out there who see their party crashing and burning around them. These middle-of-the-road Republicans, or also called moderates, are the only hope for restoring the Republicans to a state where they can effectively govern and debate with Democrats.
There are a couple of far-fetched solutions that might bring some sanity back to the House. If the Democratic House Caucus could court 18 Moderate Republicans who are thoroughly disgusted with the Tea Party Caucus, provide them some incentives to caucus with Democrats, then Democrats could shift the balance of power into the hands of Democrats. This would allow a majority of the desperately needed legislation to pass with some bipartisan support. The speakership would be reopened to election in the House, and house committees would be reshuffled to reflect the new coalition majority with some Republicans being given chairmanships, as well as some moderate legislation being pushed to the floor for a vote. This House could salvage the extremely frayed and destroyed image of the House and restore it to the institution it should be. One that passes laws, pays the bills, and moves the legislative process forward.