Sen. Rand Paul, a leading voice for conservative Republicans, said Tuesday that he would support allowing illegal immigrants already living in the U.S. to gain legal status, a potentially pivotal moment in the debate over immigration reform.

"Hispanics should be a natural and sizable part of the Republican base," Paul, R-Ky., told the U.S. Hispanic Chamber of Commerce. "But they have steadily drifted away from the GOP in each election, [and that] says more about Republicans than it does about Hispanics."

Under Paul's framework, undocumented workers who obtain legal status could eventually win citizenship, assuming they wait behind those trying to enter the country legally. It also would allow illegal immigrants to get work visas within two years.

Paul, a potential 2016 presidential contender, enjoys enormous clout with the conservative wing of his party, and his proposal could mark a sea change on Capitol Hill, where conservatives for years blocked all attempts at immigration reform because they saw any path to citizenship as amnesty for lawbreakers.

Republican lawmakers have until now been advocating the deportation of illegal immigrants and the construction of a fence along the U.S.-Mexico border, a position that prompted Hispanics, the fastest-growing electoral bloc, to abandon the GOP in droves.

"I think it's huge," said Alfonso Aguilar, executive director of the Latino Partnership for Conservative Principles. "It provides cover to other conservative Republicans who might want to speak out on immigration reform."

Paul's remarks came just a day after the Republican National Committee issued a report calling on the party to embrace Hispanics and other minorities.

Paul's blueprint did not explicitly call for an immediate pathway to citizenship -- as initial reports suggested -- and it remains more conservative than the deal being pursued by a bipartisan group of senators, including Sen. Marco Rubio, R-Fla. Paul said he remains "open-minded" about how illegal immigrants could earn citizenship.

"The main difference is I wouldn't have people be forced to go home," Paul explained. "You'd just get in line. But you get in the same line everyone is in."

Even liberal groups embraced Paul's proposal.

"The GOP should heed Sen. Rand Paul's words today and truly join the consensus that wants Congress to pass a bill that will create a just road map to citizenship, boost our economy and keep families together," the Service Employees International Union said in a statement.

But other analysts dismissed Paul's proposal as de-facto amnesty.

"It's the usual bologna," said Mark Krikorian, executive director of the Center for Immigration Studies. "This idea that there is a Republican in the heart of every Hispanic waiting to come out if we support amnesty is laughable. They're a Democratic constituency."

Paul's clout continues to grow among conservatives, particularly after waging his nearly 13-hour filibuster against President Obama's nominee for CIA director and after winning a presidential straw poll at the Conservative Political Action Conference. Still, not all of his fellow Republicans are embracing the push for immigration reform.

A group of Republican senators, including Ted Cruz and John Cornyn, both of Texas, on Tuesday called on the so-called Gang of Eight, now negotiating a compromise, to slow down work on what they called "the most dramatic and consequential alteration of our immigration system in nearly 30 years, impacting nearly every aspect of our legal and economic structure."