MIAMI (AP) — More than half of the residents in the slice of Miami that includes Little Havana were born abroad. And when Republican U.S. Rep. Maria Elvira Salazar ran for reelection last year, she won by 15 percentage points.

The GOP’s dominance of Florida’s 27th congressional district is emblematic of the party’s inroads with Latino voters in recent years in much of the U.S. and especially in Florida. Those gains helped Gov. Ron DeSantis decisively win reelection last year and contributed to the GOP taking back control of the U.S. House.

That strong showing, however, is leading to some tension as the newly emboldened Republicans in Washington aim to launch an aggressive agenda, particularly around immigration policy. Salazar is among a handful of Republicans pushing back against a sweeping proposal being considered in the House that would restrict asylum at the U.S.-Mexico border.

“We understand that immigrants want to come and live in the promised land,” Salazar said in a recent interview. “Orderly legal immigration is good for the country and good for District 27.”

Rep. Tony Gonzales of Texas, a Mexican American Republican whose district covers a long portion of the U.S-Mexico border from El Paso to San Antonio, has been even bolder, calling the legislation “anti-immigrant.”

The dissent highlights a challenge for the GOP. The party’s future may well depend on broadening its appeal beyond an aging, predominantly white base of support. And while some conservative Latinos support hard-line immigration policies, there’s a risk that the GOP could repel other persuadable Latinos by moving too far to the right on the issue.

Democrats also face political challenges on this front. The Biden administration recently proposed a measure that would impose severe limitations on asylum, arguing that surging numbers of migrants left them little choice. The push will almost certainly be challenged in court and has prompted criticism from progressives.

Republicans have long earned support from roughly a third of Latino voters, many of whom share the party’s conservative attitudes on immigration and other issues. In November’s elections, 39% of Latinos voted for Republicans, according to AP VoteCast. That was an uptick from 32% supporting Republicans in 2018’s midterm elections.

Overall, about a third of Latino voters were in favor of increasing law enforcement at the U.S.-Mexico border, while two-thirds were opposed. About half said they disapproved of the way President Joe Biden was handling border security.

Majorities of Latino voters who supported Republicans disapproved of Biden on border security and were in favor of increased enforcement at the border.

For Republicans, Donald Trump, the former president who is again seeking the White House, may have given the party something of a path on how to navigate the politics of immigration. During his previous campaigns and while he was in office, Trump embraced a crackdown on asylum rules. But he also spoke of toughening border security and building a wall. None of his actions cost him Latino support during his two elections.

“Many conservatives felt emboldened by Trump’s performance, by the idea that a Republican could be both anti-immigrant and win Latino voters,” said Geraldo Cadava, a professor of history and Latino studies at Northwestern University and author of “The Hispanic Republican: The Shaping of an American Political Identity, from Nixon to Trump.”

The immigration bill introduced by U.S. Rep. Chip Roy, a Texas Republican, would require U.S. officials to automatically ban or detain asylum seekers while their claims are being considered. Right now, asylum seekers can be released with notices to appear in court and fight for asylum. The bill would also allow U.S. immigration officials to ban all migrants from entering if there is no “operational control” at the U.S.-Mexico border.

Roy sent a letter to his GOP colleagues last week asking them to back the bill. In an interview, he said he found it “absurd” for Gonzales and Salazar to question the bill.

“A few of my Republican colleagues prefer to be fiddling while America burns,” Roy said. “Republicans are going to have to put their money where their mouth is.”

Salazar, who was backed by Trump and DeSantis, has been vocal about both the need to secure the border and the need to push for an immigration overhaul that gives some status to those who are already in the country illegally. She said she and colleagues are simply working together to make sure the proposal does not violate any laws governing asylum.

“The formula hasn’t changed,” Salazar said. “We want the Albert Einsteins of the world to come and work for us and continue to make this economy strong.”

This issue is of particular importance in her district, she said. Massive protests that erupted in Cuba in July 2021 and the government’s response to them have played a role in a more recent exodus of Cubans. Cubans are fleeing their homes in the largest numbers in six decades to escape economic and political turmoil. Most fly to Nicaragua as tourists and slowly make their way to the U.S. via Mexico.

“I do know that my district appreciates what I am saying,” Salazar said.

Some Democrats have pointed to Salazar’s comments to support their opposition to Roy’s legislation. U.S. Rep. Eric Swalwell, D-Calif., recently showed a poster board at a border security hearing featuring a quote from Salazar: “Are we stupid? Come on. This country was based on good minds. Look at Albert Einstein. We gave him a piece of paper to come in.”

Einstein arrived in the U.S. in 1933 as a refugee of Nazi Germany.

“Listen to your own colleagues, who know better about this than you,” Swalwell told fellow lawmakers.