The Obama administration suggested Tuesday that there are signs that bipartisan cooperation might be possible on immigration reform, in light of some new ideas being championed by Republican Sen. Marco Rubio (Fla.).

White House press secretary Jay Carney said that Rubio’s proposals to offer more visas to highly skilled tech workers and potentially provide legal status and citizenship to many of the nation’s 11 million illegal immigrants “bode well for a productive, bipartisan debate.”

“We hope that it signals a change in the Republican approach to this issue,” Carney said during his daily briefing, “because if we are going to get this done, it’s going to take more than just a handful of Republicans working across the aisle.”

President Obama has promised a vigorous push for comprehensive immigration reform — including a path to citizenship for illegal immigrants — early in his second term.

Rubio, a tea party favorite and potential 2016 White House contender, laid out his newest ideas in an interview with the Wall Street Journal last week. He insisted on tight border security and emphasized that foreigners who arrive legally must be treated fairly. But he split from conservatives who do not favor offering any legal status or citizenship to undocumented workers because, they say, it would reward people who break the law.

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Despite Carney’s modestly upbeat assessment, Obama and Rubio remain unlikely allies who have yet to have a discussion on immigration.

“There’s not much expectation that the White House will partner with Republicans on this,” said Rubio’s spokesman, Alex Conant. “They haven’t partnered with Republicans on anything. We’ve been working with our Senate colleagues on this.”

The ill will between Obama and Rubio dates to last summer, in the middle of the presidential campaign, when Rubio appeared to be moving toward unveiling a scaled-back version of the DREAM Act. Instead, the White House preempted the freshman senator by announcing in June that Obama would take executive action to halt the deportations of some young undocumented immigrants.

One week later, in a speech to national Hispanic leaders in Orlando, Rubio accused Obama of playing politics on the issue.

“I don’t care who gets the credit,” he said at the time. “I don’t. But it exposes the fact that this issue is all about politics for some people.”

On Tuesday, Carney said the White House is “encouraged” that Rubio’s thinking now “so closely reflects the president’s blueprint for reform.”

But Conant countered that Obama has not laid out his own proposals for a comprehensive bill.

Immigration reform advocates said the interplay amounted to early posturing for the debate ahead, with each side trying to figure out how far the other is willing to go.

Rubio is seen by many as a rising star in the GOP ranks whose personal story and influence among Latinos could help broaden the party’s appeal among minorities at a time when that population is growing quickly.

Hispanic voters largely supported Obama and other Democrats at the polls last year, and Republicans are eager to win back some of their losses. Rep. Paul Ryan (Wis.), who was the GOP’s vice presidential candidate, has voiced early support for Rubio’s immigration ideas.

“We’re seeing a sort of tango with Rubio and Obama beginning on immigration reform, and they are each not sure yet who is leading and who is following,” said Angela Kelley, an analyst at the Center for American Progress, a progressive think tank. “I suspect until they figure that out, there will be some stepping on toes.”

For the moment, the gun-control debate has overshadowed the battle over immigration reform, and some advocates have said they fear that the administration could be delayed or sidetracked by that and by negotiations with Congress over the federal debt ceiling.

But Carney said Tuesday that the administration expects the immigration debate to begin in earnest soon after Obama is inaugurated Monday.