The Plum Line says that a majority of Republicans in the House may want the Speaker of the House to pass immigration reform without support from a majority of Republicans:

But either way — however we get there — it is becoming more and more likely that the prospects for real reform turn on whether the House will pass a comprehensive bill with mostly Democratic support. There’s been a lot of speculation that this would cost Boehner his Speakership. But Boehner’s comment — that ultimately this is about “what the House wants” – is telling. If many mainstream House conservatives privately want reform to pass (without voting for it) that very well could happen, with mostly Democratic support, at no real risk to Boehner. The Speaker left the door open to that possibility today, and that’s a big deal.