Like many in his conference, Boehner has said border security must come first. And many Republicans prefer a piecemeal, step-by-step approach rather than a single big bill like the one the Senate passed.
But for many, the most vexing issue is what to do about those who are already in the U.S. illegally.
The Senate bill offers a 13-year path for most, contingent on paying fines, learning English and meeting other qualifications. Agriculture workers and people brought to the United States as youths would have a faster route.
In the House, most Republicans are reluctant to endorse citizenship for 11 million unauthorized immigrants, but also shy away from suggestions of deportation.
Ahead of Wednesday's meeting, many lawmakers seemed to be gravitating toward supporting legal status of some kind for millions here illegally. But exactly what and how were far from clear.
For some, a guest worker status would be as far as it goes, while others left open the possibility that once they're in the country legally, immigrants eventually could attain citizenship through existing channels of family or employer sponsorship. Still others were focused on citizenship for people brought to the country as youths, military veterans and perhaps others who've lived in the country for years and proven their contributions to society.
"I wouldn't prohibit forever" people from getting citizenship, said Rep. James Lankford, R-Okla. "I'm a Christian, and restitution and reconciliation's a big deal. If you do something illegal or inappropriate you should be able to resolve that, face the penalty, clear it and be forgiven."
GOP presidential candidate Mitt Romney fared abysmally with Hispanic and Asian voters last year after suggesting that people in the country illegally could "self-deport." Such suggestions have been heard rarely among Republicans since Romney's loss. But there is a hardcore group in the House that opposes any legal status for people here illegally.