WASHINGTON (TNS) For all of Donald Trump's heated rhetoric about immigrants, he still beat Mitt Romney's 2012 showing with Latino voters last November, exit polls show.

But after the White House this week threw its support behind a proposal that would drastically reduce legal immigration, Latino Republicans are warning anew about the political perils of Trump's hardline position — for him, and for the rest of the party.

"When you win the presidency, everybody thinks everything is all right, but I'm worried about Texas going the route of California," said Artemio Muniz, the Texas chairman of the Federation of Hispanic Republicans.

On Wednesday, the White House touted its support for a new immigration overhaul proposal that appears set to reduce legal immigration by half over the next 10 years through stringent restrictions on the kinds of immigrants who could enter the country. That proposal has a tough road ahead in Congress, but Republican operatives and leaders intimately familiar with the Hispanic community say that support for such an approach is another step backward when it comes to improving the GOP's generally dismal standing with Latinos at the national level.

"I don't want to say Hispanics vote exclusively on immigration, that's not true, but it does hurt him with the Hispanic community," said Alfonso Aguilar, president of the Latino Partnership for Conservative Principles, who yanked his support for Trump after a particularly hard-edged immigration speech last August but has since often emphasized areas of agreement with the administration. "It goes beyond the Hispanic community. It's what our country is all about."

Hard-line positions on immigration didn't ultimately stop Trump in November, but Latino Republicans say there's little reason for complacency: The 29 percent support he notched from the Latino community, while slightly better than Romney's results according to exit polls, still falls behind Sen. John McCain's 31 percent standing, and well behind President George W. Bush's 44 percent support from the community in 2004.

"While the math worked in 2016, it's not sustainable for Republicans to do that poorly with Latinos," said Jacob Monty, a Houston attorney who, like Aguilar, backed away from Trump late last summer, but is quick to note areas where Trump deserves credit as president now.

Juan Hernandez, who ran Hispanic outreach for McCain's presidential race and has long been involved in efforts to encourage more Hispanic Republicans to run for office, said that Trump's rhetoric makes it increasingly difficult to make the case for other Latinos to jump in as Republicans — and the latest proposal further complicates that mission.

"We were doing very well getting Hispanics to run for office in the last decade, six years, but I know many would tell me, 'Look, how can I run with a big R on me, when the president is a Republican and is insulting my family, my friends from the south, and the values we've held related to NAFTA, related to hard work?'" Hernandez said, noting he has had that conversation with a number of potential candidates, though he declined to name names.

Meanwhile, several Latino Republican lawmakers who are in office were quick to push back on the plan.

"I oppose #RaiseAct bc it will destroy opportunities 4 immigrants who follow the rules + positively contribute 2 our American way of life," tweeted Rep. Ileana Ros-Lehtinen, R-Fla.

Added another Miami-area congressman, Rep. Carlos Curbelo: "If the goal is more young immigrants who speak English & can contribute to American society, start by documenting the ones already here."

And a number of Latino Republican leaders said Trump could earn significant goodwill if he offered real support of the DREAM Act, which would offer a pathway to permanent legal status for those who were brought to the United States illegally as children, a group for whom Trump has expressed some sympathy, though his White House has indicated little appetite for the DREAM Act. Either way, the focus on curbing legal immigration instead is a "misplaced priority," Monty said.

"He could bring a lot more people on board, he could show a willingness to solve urgent problems, he could get a huge win under his belt and rebuild trust with the Latino community," Monty said. "If he lets that DREAM Act issue pass, I believe it will be a lost opportunity."

Muniz fretted that there is little sense of urgency to improve GOP standing with the Latino community right now because Trump won. But he noted that drilling down into the numbers reveals that he underperformed in heavily Latino counties in Texas and elsewhere. The latest proposal is not going to help the Republican brand, he said.

"A lack of understanding is putting us in danger in Texas, Colorado, Arizona — in danger politically," he said. "That's the concern I have. You've got to have a majority coalition for the future. It's very difficult to convince people when Trump takes the presidency without the Hispanic vote. It's a tough position to be in."

Added Lionel Sosa, a veteran operative with a long history of helping presidential candidates with Hispanic outreach before Trump came along: "He keeps working the base, and that's good, that's where he has the support. The question is, will the base get smaller as he goes forward or will he be able to keep it all? He has to keep 100 percent of the base to be successful. He certainly doesn't have 100 percent support of the Republican Senate, that's an indication of the way people generally feel around the country."

Certainly, not every Latino leader was ready to blast the new immigration proposal.

"While I have many disagreements with the current proposal, I am hopeful it will spur Congress to act with urgency to pass comprehensive immigration reform," read a statement from the Rev. Samuel Rodriguez, the president of the National Hispanic Christian Leadership Conference, who offered a prayer at Trump's inauguration.

And Al Cardenas, a former American Conservative Union chairman who has worked extensively on immigration reform efforts, said that some of the proposals in the plan could be acceptable — if they were part of a broader comprehensive immigration reform package.

"If you package it all, you negotiate a give-and-take, that's what problem-solving is all about, I could see it, but it ought to be part of a bigger conversation," said Cardenas, who doesn't shy away from criticizing Trump when he disagrees. "Standing alone, I wouldn't urge members to vote for it."

But beyond the policy details, Hernandez said he worries about the message that the latest immigration proposal sends about the Republican Party's attitude toward immigrants in general.

"My party is in grave danger," Hernandez said. "Our brand is one that, to be honest, is an embarrassment."