What would Republican-led immigration reform look like?

In the week since President Barack Obama won the election thanks in part to the Hispanic vote, a handful of top Republicans are breaking with the party line and floating the idea of working with Democrats to reform the nation's immigration system.

The presidential election was "a wake-up call," explains Jennifer Korn, executive director of the Hispanic Leadership Network and former director of Hispanic and Women's Affairs in the Bush White House. (Former Gov. Mitt Romney got 27 percent of the Hispanic vote on Nov. 6; if he had managed to nab just 35 percent—a share George W. Bush exceeded two elections in a row—he would have won the popular vote.)

That wake-up call, however, doesn't mean Republicans will necessarily support immigration reform models as liberal as those pushed by both Bush and Ronald Reagan—models that included citizenship for illegal immigrants who met certain conditions. And some conservatives have signaled that in order to sign onto reform, they would want big concessions in return. The proposals would no doubt anger Latino advocacy and immigrant rights groups—which in the past have said immigration bills must offer full citizenship or immigrants will be relegated to "second-class status"—as well as set the stage for clashes with pro-reform Democrats.

Sen. Rand Paul, R-Ky., told Politico that he's open to giving illegal immigrants a path to citizenship in exchange for a temporary moratorium on all legal immigration while they "assimilate." Sen. Lindsey Graham, R-S.C., a longtime proponent of reform, said legalization should be paired with the repeal of the 14th Amendment, which guarantees citizenship to anyone born on U.S. soil. And Republican House Speaker John Boehner told reporters on Friday that he would not commit to including a path to citizenship in his immigration reform efforts.

Meanwhile, the conservative political commentator Dick Morris proposed in an op-ed in The Hill that immigration reform should not offer any eventual citizenship to illegal immigrants. Instead, Congress should allow people living in the country without permission to apply to be a temporary guest worker.

But it remains to be seen how serious Republicans are about these proposals. Neither Democrats nor Republicans have yet to put forward a draft version of a bill, and it's unlikely any will emerge until after they deal with the "fiscal cliff" negotiations. At his press conference on Wednesday, President Barack Obama said negotiations would begin shortly after his inauguration and Congress should "seize the moment" to overhaul the creaky immigration system.

In the past, Republican presidents have taken the lead on immigration. Reagan was the first to tackle the issue comprehensively with his 1986 immigration bill that eventually gave more than 3 million illegal immigrants citizenship. (The law was later criticized as an "amnesty" that did not deter future migrants from illegally crossing the border.) Almost 20 years later, Bush took up the cause again and, in an effort to rebrand Reagan's plan, proposed a bill that beefed up border security in addition to legalizing illegal immigrants. The idea was that the law, unlike Reagan's, would prevent future illegal immigration from taking place.

But Republicans—and a few Democrats—weren't buying it. A conservative grass-roots opposition to Bush's plan emerged, fueled by volunteer Minutemen who patrolled the border to try to deter illegal crossings. Some Democrats, meanwhile, were swayed away from the bill by concerns from unions that the law would empower companies to hire cheaper nonunion labor. In 2007, 15 Democratic senators joined 37 Republican senators to block the bill, forcing Bush to concede defeat.

Since 2007, the Republican Party has moved far to the right on the issue, with Romney memorably saying illegal immigrants should "self-deport" and he would oppose any bill that sought to give them legal status. Since his crushing defeat, several conservative leaders have said it's time to rethink this stance, including Fox News analysts Sean Hannity and Charles Krauthammer. (This prompted Ali Noorani, head of the liberal National Immigration Forum, to joke that Fox News had become an "an immigrant rights activist center.")

On Friday, Boehner said any approach to immigration would be step-by-step, adding that he would not commit to including a path to citizenship for illegal immigrants in the bill. "I'm not talking about a 3,000-page bill," he told reporters. "What I'm talking about is a commonsense, step-by-step approach to secure our borders, allow us to enforce the laws and fix a broken immigration system."

Republicans who sign on to reform must find a way to avoid the base-riling label of "amnesty" to attach to their bill, cautioned Korn. She said Bush's immigration effort in 2006 was doomed when people started calling it amnesty. "The whole 'pathway to citizenship' got people upset, because people thought, 'Oh, undocumented immigrants are going to become citizens.' That was not the case. They were going to have a temporary visa, then they were going to apply to be legal residents. We're talking a 15-year process," she said. Though immigrants would eventually have been able to apply for citizenship under Bush's law, it was not quick nor automatic.

Republican Rep. Mario Diaz-Balart of Florida said he is already having conversations with other lawmakers about immigration reform, but that it's "premature" to talk about whether any bill would include a path to citizenship.

"It's absolutely doable," he said of passing reform.

Diaz-Balart added that the president must become involved for any bill to pass. "Something of this magnitude has to be done at a bipartisan level," Diaz-Balart said. "It's going to require [Democrats] to actually want to solve the problem and not just stir it up."

The president said during the campaign that not passing immigration reform was his greatest failure in his first term. At his press conference on Wednesday, he said he was "confident" it will pass this term and laid out his plan for how the bill would deal with the illegal immigrants who already live in the country. "It's important for them to pay back taxes, it's important for them to learn English, it's important for them to potentially pay a fine, but to give them the avenue whereby they can resolve their legal status here in this country, I think is very important," he said.

Juan Hernandez, a Texas-based Republican political consultant who served as Sen. John McCain's director of Hispanic outreach in 2008, said whatever the potential disagreements, congressmen should start hammering out a deal now.

"Should it be with two, three or four steps? That's fine. Let's negotiate. But let's starting taking the first steps immediately," Hernandez said. "We may not find a political moment again in which at least I see everyone saying it's time for immigration reform."