A Texas restaurateur and longtime Republican faced an uncomfortable question from one of his Latino cooks: “How can you be a Republican when Republicans hate Hispanics?” the employee asked in 2011, as the party’s presidential hopefuls battled for the nomination.

Brad Bailey’s car is adorned with GOP bumper stickers. He frequently hosts Republican fundraisers at his two Houston seafood restaurants. But this spring, he took a leave of absence to try to shift his party’s stance on immigration. “I started looking at the debate through the employees’ eyes,” recalled Bailey, who founded The Texas Immigration Solution. “This is not Republican at all. … This issue, this one issue, is turning people off.”

He met Friday with aides to Republican Sen. Marco Rubio of Florida, who is emerging as the party’s biggest champion of a comprehensive rewrite of immigration laws.

Bailey’s group, which successfully lobbied to get a guest worker program on the national party platform, is part of a larger movement to pressure Republicans to negotiate an overhaul of the immigration system. The activists say outspoken anti-immigration groups within the GOP have made the issue toxic for vulnerable lawmakers who fear more conservative primary challengers and, even worse, have alienated the fastest-growing minority in the country.

“There is a large number of Republicans across the country whose voices have been out-shouted by the angry nativists and anti-immigrant activists of the far right,” said Fergus Cullen, a New Hampshire strategist who recently founded the group Americans by Choice.

The activists generally support proposals similar to the those Congress took up in 2007, including a comprehensive package that would include a guest worker program, an overhaul of the visa system and some sort of path to citizenship, or legal status, for undocumented immigrants. They are likely to run into opposition from groups such as the Federation for American Immigration Reform, which argues such plans will incentivize illegal immigration.

“The immigration policy positions of the Republican Party have nothing to do with the problems they have with the Hispanic voting population,” FAIR President Dan Stein said. “They have a low-skilled worker problem.”

The activists’ efforts are bolstered in Washington by a broad range of industry groups, prominent conservatives such as Americans for Tax Reform President Grover Norquist and the U.S. Chamber of Commerce.

“All of the Hispanic groups, the agriculture groups, the religious groups are ready,” said Jennifer Korn, who helped shape immigration proposals under President George W. Bush. “What we had in 2007 was coalitions put together at the White House. Now these efforts are popping up organically.”

Korn is executive director of the Hispanic Leadership Network, an outgrowth of the American Action Network, which spent almost $12 million in support of Republican congressional candidates last cycle.

In recent weeks, Rubio and former Florida Gov. Jeb Bush have thrown their weight behind such a broad-based approach. Former Commerce Secretary Carlos Gutierrez has launched a super PAC dedicated to the cause, though it has yet to raise any funds, according to the Center for Responsive Politics.

Galvanized by the signs of Republican support, leaders from labor, law enforcement, civil rights and evangelical groups, among others, argue that a comprehensive immigration plan is a national imperative and that consensus is within reach. At a news conference in Washington last week, Chamber of Commerce President Thomas Donohue echoed the White House’s warning that without a comprehensive package, some of the more controversial components of an overhaul could be left by the wayside. Donohue has been working with AFL-CIO President Richard Trumka to resolve differences over how foreign workers can come to the U.S. for temporary employment, the major sticking point between the powerful business and labor lobbies.

Such budding alliances, and a growing army of Latino activists, are giving Hispanic advocacy groups clout with both parties. “Any position where both parties see you as discerning, as holding you accountable, is a good position,” said Clarissa Martinez de Castro, the director of immigration policy at the National Council of La Raza. “Doing something is the expectation. … We believe that the people who work to get this done should get rewarded.”

While Congress is consumed by the sequester, gun policy and budget standoffs, the groups hope to spend the coming months lobbying lawmakers in Washington and in their districts.

The National Council of La Raza is bringing about 400 Latino activists to Capitol Hill on March 6. In the meantime, it is continuing voter registration efforts and in-district education. The AFL-CIO will soon unveil a national mobilization campaign in support of a pathway to citizenship, which it says is its top national priority for 2013.

On the right, activists such as Bailey and Cullen are working with conservative think tanks and others to try to convince GOP lawmakers that an immigration overhaul is a political imperative. “We can’t be the party of ‘we the few,’” Bailey said. “It must be ‘we the people.’”