In recent days, Mr. Rubio has begun to sound nervous again when it comes to the immigration legislation. He sent a letter to Senator Patrick J. Leahy, the Vermont Democrat who is chairman of the Judiciary Committee, counseling against “excessive haste” in changing immigration law. On Sunday, just moments before two of his fellow bipartisan group members were set to appear on NBC’s “Meet the Press,” he released a statement that warned, “No final agreement on immigration legislation yet.”…

Democrats in the bipartisan group say they understand that Mr. Rubio is in a politically tight spot, and are willing to give him more leeway to publicly question aspects of the process, because they believe he will be instrumental to the bill’s success. After the bipartisan group introduces its legislation, they hope Mr. Rubio will play high-profile role in selling their overhaul to reluctant Republicans.

Still, Mr. Sharry, the immigration advocate, said Mr. Rubio could raise only so many objections to an immigration overhaul before he starts to look like “the boy who cried wolf.”

“It’s like, dude, chill,” Mr. Sharry said. “Yes, you are uniquely qualified to be a conservative fighting for immigration reform that comports with conservative values.”