Proposals to increase security along the U.S.-Mexico border and whether to legalize 12 million immigrants in the U.S. illegally have divided Republicans, who are trying to win more support from minority voters. Party leaders in the House say they won't negotiate on a Senate bill, which passed that chamber with bipartisan support last year, that would grant a path to citizenship.

Closed Doors

Still, bipartisan conversations are taking place behind closed doors. Senator Charles Schumer, a New York Democrat, and Republican Representative Paul Ryan of Wisconsin have met on the topic, said Kevin Seifert, a Ryan spokesman.

House Minority Leader Nancy Pelosi said Jan. 29 that she and House Speaker John Boehner spoke about immigration policy before a Republican policy retreat last week.

Diaz-Balart praised Obama for lowering the "emotional decibels" last week, when the president said he'd be willing to consider a House plan that stopped short of granting a path to citizenship to 12 million undocumented immigrants in the U.S.

"It's the right tone," Diaz-Balart said. "You have to lower the rhetoric, lower the tone, lower the emotional decibels. And I think he's been doing that recently on immigration reform."

Boehner told reporters today that "members seemed to be rather supportive" of the draft principles on immigration and that no decision has been made on legislation.

Boehner's immigration framework, released last week during the retreat in Cambridge, Maryland, would legalize undocumented workers in the U.S. and grant citizenship to those brought to the country as children.

Once undocumented immigrants were legalized, they could seek one of the currently available paths to citizenship, Diaz- Balart said.

That approach may permit between 4.4 million to 6.5 million undocumented immigrants to gain lawful residence, according to the National Foundation for American Policy report last month. The Senate bill would make citizenship available to about 8 million immigrants, according to the Congressional Budget Office

The immigration debate has split the Republican Party.

Business groups, including the U.S. Chamber of Commerce, the largest business-lobbying group, have pushed for immigration-law revisions as a way to spur economic growth.

Heritage Action

Groups including Heritage Action, an advocacy group that supports candidates tied to the small-government Tea Party movement, maintain that advancing immigration measures risks taking the focus off Obamacare's troubled rollout.

Diaz-Balart said he'll seek support by making the argument that there'll never be a perfect time for immigration legislation.

"There is no secret the GOP brand is not very good with women, with minorities, with a number of groups, he said. ''Politically, taking it off the table helps us.''

Reaching out to minority voters was a top recommendation of a Republican National Committee report after their party's presidential candidate, Mitt Romney, won just 27 percent of the Hispanic vote in 2012.

The number of eligible Hispanic voters rose 19 percent to 23.3 million in 2012 from 19.5 million in 2008, according to a June report from the Pew Research Center. The number of white voters declined for the second presidential election in a row.

Still, Republican lawmakers who support a path to citizenship often risk a backlash. Senator Marco Rubio, who helped craft the Senate immigration bill, fell from first to fifth in a poll of nine potential Republican candidates in Iowa, the state that holds the first contest every four years, according to Public Policy Polling surveys.

Rubio now backs House Republicans who refuse to negotiate over the Senate bill in a conference committee.

''One massive piece of legislation — not just on immigration reform but on virtually any issue — it's not going to pass given this political climate and this Congress," Rubio said Jan. 29 at a Wall Street Journal breakfast in Washington.