Eddie Carmona, the campaign manager for the Campaign for Citizenship, another advocacy group, said Mr. Boehner’s blueprint was “outrageous.” Richard L. Trumka, the president of the A.F.L.-C.I.O., called it “a flimsy document” and “half-measures that would create a permanent class of noncitizens without access to green cards.”

Representative Luis V. Gutierrez, Democrat of Illinois, said in a conference call with reporters that members of the coalition that is pushing for an immigration overhaul should be willing to consider Mr. Boehner’s approach.

“If your standard is citizenship for everyone immediately or no immigration reform at all, you are going to get no immigration reform at all,” Mr. Gutierrez said. “People are going to have to stand in the middle and leave the comfort of their caucus.”

During the online meeting, the president said he wanted to engage the Republicans. “I don’t want to prejudge and presuppose,” he said.