She has rolled out a plan that would offer deportation protection to so-called Dreamers brought into the country illegally as younger people and a 10-year path to achieving a renewable legal status for employed undocumented immigrants with a clean criminal record. Salazar's approach also expands visas for agricultural workers and boosts border security, a must-have for nearly all of her party.
Giménez, a previous Miami-Dade mayor, has offered a less sweeping overhaul that would still represent a huge step forward for the post-Trump GOP. His proposal would allow undocumented immigrants already working in the U.S. to pursue a pathway to citizenship by applying through their country of origin, without having to return to their countries to do so. Gimenez's plan would effectively sweep them into the current system without putting them ahead of anyone else seeking legal immigration status.
“To me that's a much simpler way," Giménez said in an interview. "Different countries have different quotas. Some people may make it to citizenship and some people may not, but I'll tell you what — I think that most of the undocumented immigrants here, all they want to do is go out in the light."
“There's a practical impossibility to deporting them,” he added. “They're a productive part of our society for the most part."
Salazar and Giménez have some support in urging their party to do more than amplify hardline Trump-era messaging on migration deterrence. Eight House GOP colleagues and onetime immigration deal-maker Sen. Lindsey Graham (R-S.C.) have backed Salazar's proposal, for example. But amid rising crossings this year, most Republicans are clinging to their demand that the Biden administration address border security before they'll work on a more wide-ranging immigration bill.
Salazar and Giménez's efforts follow past Republican-driven attempts on immigration reform have failed miserably. The most recent try in 2018 was voted down by a wide margin, after more than a month of negotiations between conservative members of the House Freedom Caucus, more immigrant-friendly moderates and GOP House leadership.
That leaves the party's aspiring immigration reformers with fewer tools to get a broader coalition of Republicans on board.
“Republicans are more unified than ever before that amnesty is a non-starter and we must secure the border,” said Republican Study Committee Chair Rep. Jim Banks (R-Ind.), whose caucus is the largest in the House GOP.
The RSC has played a key role in shaping GOP messaging on immigration, including the development of a framework shared with leadership that Banks described as "guardrails for any future immigration deal.”
House Republicans have repeatedly highlighted signs of the Biden administration's struggle to contain rising migration, a message they see resonating with their base. Their members on the Oversight and Reform Committee, for example, have sent three letters to the panel's Democratic chair in recent weeks pushing for a hearing on the border.
Polling suggests that the party's core voters are indeed closer to Banks than Salazar and Giménez on immigration. When the nonpartisan Pew Research Center the previous month asked if it was important to reduce the number of people coming to the U.S. seeking asylum, 78 percent of Republicans said yes — compared with 39 percent of Democrats.
A clear majority of Americans surveyed by Pew also were critical of the government's work handling the recent uptick in migration, with 68 percent of respondents saying it was doing a very or somewhat bad job at the border.
Salazar counters that her plan, which calls for “triggering mechanisms” to be in place to ensure border security is addressed before other reforms can take place, will also help her party connect with voters. Several undocumented immigrants seeking a path to legal status identify with the GOP brand of limited government and consider themselves oriented with traditional faith-based values, she says.