“Discharge petitions are difficult, but when they work, it’s because there’s a clear majority of the body that supports a specific proposal, and in this case, that is true,” Mr. Schumer said. “But I have no illusions that this will be easy in any way.”

J. Dennis Hastert, Republican of Illinois who was speaker the last time a discharge petition succeeded, was critical of the tactic. “I have always been an advocate of regular order,” Hastert said. “Discharges, I believe, lead to poor results.”

Coming on the heels of a “clean” debt ceiling vote this week, which Mr. Boehner put on the House floor on Tuesday knowing it would pass only with a majority of Democratic votes, Mr. Schumer’s suggestion also serves as a test of just how far Mr. Boehner is willing to push his conference and buck outside conservative activists. Mr. Boehner has already, six times in the past 14 months, violated the unofficial House Republican credo that legislation should pass the House only with a majority of the majority, and a discharge could potentially provide him the opportunity to do so on immigration.

Yet that option remains highly unlikely. Representative Charlie Dent, a Republican moderate from Pennsylvania and a supporter of moving forward on immigration, said a discharge petition has “zero” chance of accumulating the Republican signatures it would need. Even Republicans like him, who favor action, would not sign on to a petition requesting consideration of the Senate-passed bill, because they do not support it on policy grounds.

During the 16-day government shutdown in October, Democrats circulated a discharge petition to reopen the government — a maneuver that was seen as far more urgent and, in theory, had far more support. But Republicans refused to sign, said Mr. Dent, who led the House Republicans trying to end the shutdown.

Now, the same Republicans who support action on immigration would not betray Mr. Boehner. “It means you’re putting a thumb in the eye of the speaker, not just in this issue but any issue,” Mr. Dent said. “You’re essentially handing control of the floor to the minority party.”

The speaker’s decision this week to put a debt ceiling increase to a vote without preconditions was meant to get past a divisive issue so Republicans could regain their focus on the issues that unite them, especially opposition to President Obama’s health care law. It was “pulling the bandage from the scab and doing it fast,” Mr. Dent said, adding that Republicans were not about to do the same thing with immigration anytime soon.