The House has its own bipartisan Gang of Eight, which has been meeting on and off for nearly four years to craft a comprehensive immigration reform bill.
The group of four Democrats and four Republicans announced they had reached a deal in principle last week. But that pronouncement now appears to have been made prematurely.
Politico reports that lawmakers agreed on a compromise over whether immigrants applying for citizenship should receive government-subsidized healthcare. But other significant issues remain unresolved, like provisions around border-security.
If the group is unable to agree on a comprehensive proposal, that could lead to a flood of bills that deal with immigration issues on a piecemeal basis. Some House Republicans prefer to tackle immigration issue-by-issue, but Senate leaders have called that approach a non-starter, fearing that a pathway to citizenship -- crucial for Democrats -- could be left aside.
Theoretically, the Senate bill could be reconciled with a series of House bills. But judging by the level of dysfunction in Congress, that approach would have a slim chance of succeeding.
Boehner may have summed it up best on Thursday, when he spoke to reporters at his weekly press conference.
"The House will work its will," he said. "Don't ask me how because if I knew I'd certainly tell you."