There would have to be a conservative that sufficient House members would all unite behind to elect as Speaker. To my knowledge no one has announced they will take on Boehner. Perhaps Paul Ryan would be a logical choice since he was the VP nominee after all and has mass name recognition. But whoever it is it has to be someone most Republican House members can support. Who is this person who has agreed to run against Boehner? Time is running out
Until there is someone to actually challenge Boehner then all of this is just academic
Somewhere about 40 years ago there was a delightful scheme to depose a Demonrat Speaker (Carl Albert?) by forming a majority made up of the GOP Caucus and Southern Democrats (then far more conservative than now). It would have required 40 Democrats or thereabouts. To obtain their votes, the GOP Caucus would have had to agree to elect the quite conservative Congressman Joe Waggoner of Louisiana as Speaker and Waggoner would have had to agree to name many conservative GOP members as committee chairs in a fair division of such patronage between GOP and conservative Democrats. The effort failed and Waggoner retired at the end of that term.
I live in an Illinois district just south of Ryan's Wisconsin district. Ryan has a decent voting record and is certainly more palatable than Boehner, Cantor and McCarthy but, if conservatives are going to topple the leaders, they should seek a better candidate than Ryan who, whatever his voting record, is a suck up for leadership. He joined with leadership in purging my Congressman Don Manzullo (22 years of superb service) in favor of Adam Kinzinger, a carpetbagger from Chicagoland, who was originally elected in a Joliet district by the Tea Party and stabbed the TP in the back immediately upon arriving in DC.
The leaders handed Kinzinger $600 K in special interest money from out of state corrupt interests to dispatch Manzullo with a blizzard of outright lies. This resulted from Manzullo writing to Boehner a public letter one year ago asking that Congress be called back into session to pass a resolution telling Boehner's pal Obozo that there would be no more debt limit increases. No increase in debt limit would mean fewer of our tax dollars being squandered on bloated corrupt special interests of all stripes such as feed the coffers of the leaders of BOTH parties. Gee, Boehner, Cantor and McCarthy would have less mad money to play with if the GOP caucus actually took the public's interest as its own.
The only part of Boehner's purge of GOP Congressmen that might have been justified was purging Weepy Walter Jones of North Carolina, a real mushball particularly on war, defense and foreign policy. Of course, those would not be Boehner's reasons. Instead, even Weepy Walter was purged for not being on board with Weepy John Boehner's craven sell outs on matters of importance to the rich and corrupt and to the Obamacrats.