There are two solutions to this. Republican congressmen need to grow a pair and deal with the consequences of losing if that happens or have a secret ballot to elect party leadership. I don't like the latter option since I want to know how my rep voted.
The moment after my rep was reelected (actually after I got home from the bar on election night), I sent him an email telling him that in no uncertain terms that if he votes for Boehner that he will never have my support again. Flash forward from election night to two weeks ago ... I heard my rep on local talk radio saying how he doesn't want to vote for Boehner, but there was no one running against him. So the choice was between Pelosi and Boehner and he would vote for Boehner. I can't fault him in that choice, but I still have to wonder why he and other Republicans don't get together and put up some kind of fight. I swear most Republicans are a bunch of limp-wristed expletives.
I have heard similar. No one wants the job.
This is a leaderless party, and no one wants to lead it.
The GOP is not part of any solution to any problem.
The Republican Caucus in the House already had its nominating election for House leadership positions in November. Boehner was the only candidate running for Speaker and he was nominated, unanimously, on a voice vote.
It will be Boehner versus Pelosi for Speaker when the House reconvenes in January. The vote is likely to be something flose to 247 Boehner/188 Pelosi.
Aside from Boehner as Speaker, the House majority leadership will be:
Majority Leader: Kevin McCarthy
Majority Whip: Steve Scalise
Majority Chief Deputy Whip: Patrick McHenry
Conference Chair: Cathy McMorris Rodgers
Conference Vice-Chair: Lynn Jenkins
Conference Secretary: Virginia Foxx
Campaign Committee Chairman: Greg Walden
Policy Committee Chairman: Luke Messer
Senior Deputy Whip: Ann Wagner