His position was echoed Tuesday by House GOP lawmakers on the key Judiciary Committee, who signaled openness to providing legal status to the roughly 11 million people in the country illegally, while characterizing the idea of eventually granting them citizenship as "extreme."
That stance breaks with not just President Obama and Democrats but also Senate Republicans, particularly Sens. Marco Rubio (FL), John McCain (AZ) and Lindsey Graham (SC), who have backed a pathway to citizenship to undocumented immigrants if they pass a background check and pay a fine and back taxes. Polls show broad support for the idea.
Rubio this week defended his approach as "humane" and said it "respects the rule of law."
Fifty-six percent of Americans want to offer illegal immigrants a path to citizenship, according to a Quinnipiac survey released Thursday. Just 10 percent say they should be allowed to stay but not apply for citizenship, and 30 percent say they should be forced to leave.
Some immigration reform advocates rule out anything less than eventual citizenship.
"I think it would be wrong for us to create a permanent underclass of people who live in this country who never can reach American citizenship," said Rep. Luis GutiÃ©rrez (D-IL). "I want them to have all the responsibilities and obligations that come along with American citizenship."
"Not only is second-class status a bad policy option, it's bad politics for the GOP," said Frank Sharry, executive director of the pro-immigration America's Voice. "It tells Latino, Asian, and immigrant voters that their loved ones are good enough to cook for us, clean for us, and take care of our children, but they can never become one of us."
On NPR, Labrador called on Democrats to decide whether they wanted "a political victory or a policy victory."
"If they want a political victory they're going to draw a fine red line and they're going to say, either a pathway to citizenship or nothing else," he said. "They know that the Republicans in the House are not going to be able to vote for that, and then they're going to be able to beat us over the head in 2014, and say, look, the Republicans don't like immigrants. Which is not true."
"This is not about politics," he said. "In fact, as Republicans we need to understand that we're not going to get any benefit from fixing the immigration system. I think the Democrats at this point, because you have the president who's in power, are going to get all the accolades. We just need to do this because it's the right thing to do."