So far, Mr. Rubio has seen early success wooing grass-roots Republican voters. When he joined the bipartisan group late last year, after Mitt Romney lost the presidential election in part because he was overwhelmingly rejected by Hispanic voters, Mr. Rubio quickly went on a one-man blitz of conservative news media outlets, explaining his guiding immigration principles and winning plaudits from the likes of Rush Limbaugh and Sean Hannity.

“The argument is that it’s not conservative policy to have 11 million illegal immigrants in this country,” said Phil Musser, a Republican consultant and former executive director of the Republican Governors Association. “By showing up and by boldly deciding to engage people who have had their fingers in their ears on this issue, he’s been able to decalcify a process that’s been stuck for a long time.”

He and his staff have studied the mistakes of the last attempt at immigration overhaul, in 2007, and have tailored their pitch to address conservative concerns. Mr. Rubio stresses that strict goals for border security must be met before any illegal immigrants can be put on a path to citizenship. And he talks of refining the current system — from increased enforcement to a workable plan for future legal immigrants — saying he wants to ensure the country does not face another wave of illegal immigrants down the road.

“His emphasis on strong border security and enforcement is a big deal, and I think the Democrats are finally beginning to get that, and I think that is because of his strong leadership and communication skills,” said Mel Martinez, a former Republican senator from Florida who was part of the failed 2007 attempt at an immigration overhaul.

In calling for a full committee review, Mr. Rubio also hopes to prevent the dynamic that helped kill the 2007 bill — the impression the immigration proposal was written in secret, then rushed to the Senate floor.

Mr. Rubio has also been active behind the scenes. In one-on-one phone calls and meetings, he has continued to regularly reach out to conservative news media outlets, grass-roots supporters and House Republicans. (“By the way, I spoke to Marco Rubio today about this off the air,” enthused Mr. Limbaugh on his show Thursday. “He’s insistent this thing not be ramrodded through, that there be hearings.”)

In January, Mr. Rubio brought Enrique Gonzalez, a well-known immigration lawyer based in Miami, onto his staff full time, and has assigned a legislative assistant to work nearly exclusively on immigration issues.