That's not how Speaker election works. All members of the House vote, not just the majority party.
Party members are expected to vote for their party nominee, or at least someone in their party. But, there's an "escape clause": all Boehner needs is for enough Democrats to vote "present" or abstain. The Speaker only must receive a majority of the votes for an individual. "Non-votes" aren't counted.
If Boehner doesn't get a majority vote on the first ballot, I think it's almost certain that he will get a majority on the second ballot, either through explicit votes from Democrats or by abstentions. The election process and history is discussed here:
http://en.wikipedia.org/wiki/Speaker_of_the_United_States_House_of_Representatives#Selection
But would JB waltz into that trap? Could he bear the headline Boehner Retains Speakership with Democratic Support? America just ousted as many RATS as possible. If their House of the People is usurped by the RATS they just pulled the rug under, won’t the impetus to primary Boehner and his apparatus skyrocket to the top of the electoral to-do list?