WASHINGTON — A newly formed group of House Democrats is seeking to shift the party’s positioning on immigration to the center and address a major vulnerability for President Joe Biden that could shape his prospects for re-election this fall.

The “Democrats For Border Security” task force is co-chaired by Rep. Henry Cuellar, D-Texas, who represents a border district, and Rep. Tom Suozzi, D-N.Y., who flipped a Republican-held swing district after campaigning on his support for tougher border laws.

One thing they have in common: They’re fed up with the party’s leftward turn on immigration over the last decade and want a course change to emphasize enforcement. Cuellar’s calls for tougher immigration laws date back years. Then Suozzi successfully deployed it in the suburbs of New York. They both say Democrats must do the same to win competitive House districts and defeat former President Donald Trump this November.

“I think it’s a pretty good pathway for Democrats. Don’t cede the narrative to Republicans when it comes to border security,” Cuellar said in an interview. “It doesn’t matter if we’re Hispanics. We want to see order. We want to see security.”

A late-January NBC News poll found that Trump has a 35-point advantage over Biden among voters asked who they believe will do a better job at “securing the border and controlling immigration.” Trump and Republicans are putting a heavy emphasis on a border crackdown as their pitch to voters in the 2024 election.

In his special election last month, Suozzi sought to flip the script by going on offense with border security, embracing a bipartisan bill to impose tougher asylum laws and depicting his Trump-aligned opponent as seeking to exploit the issue for political gain. He also called for more legal pathways for aspiring Americans. It worked.

The New York Democrat said he has told the White House that Biden can replicate his strategy successfully all over the country. And he believes the president has begun to do it.

“I think Democrats are already changing,” Suozzi told NBC News. “Democrats have always been concerned about border security, but now they’re being more vocal about it and proactive about it. And I think the president is doing that.”

The new caucus includes 26 members including a host of Democrats in tough districts, including Reps. Matt Cartwright, D-Pa.; Angie Craig, D-Minn.; Jared Golden, D-Maine; Susie Lee, D-Nev.; Steven Horsford, D-Nev.; Mike Levin, D-Calif.; Jared Moskowitz, D-Fla.; and Mary Peltola, D-Alaska. It also includes Reps. Ruben Gallego, D-Ariz., and Colin Allred, D-Texas, who are running for Senate in border states where immigration looms large for the electorate.

“Look, some of the loudest voices on the border crisis have made clear they have no interest in solving it,” Gallego said. “The Arizona border leaders and law enforcement I’ve met with are tired of it. We need to cut through the noise and get a border security bill done.”

Progressive leader: We ‘can’t be Republican Light’

Some progressives are uneasy with the shift. Rep. Pramila Jayapal, D-Wash., the progressive caucus chair, said Democrats “can’t be Republican Light on harsh enforcement policies” after they ran in 2020 against Trump’s border policies. She wants Democrats to “start making the connection between chaos at the border and chaos in the legal immigration system.”

She added: “I’ve asked the White House to not use some of those harsh statements and instead focus on Republican hypocrisy.”

The leftward shift traces back to former President Barack Obama’s second term after he dominated with Hispanic voters in 2012. A popular narrative formed that a more liberal immigration stance was key to winning more Hispanic voters. Democrats, egged on by activists who criticized Obama as too tough on deportations, de-emphasized punishment for lawbreakers and focused their rhetoric on creating pathways to citizenship.

But over time that narrative fell apart, as the asylum system became overwhelmed with more migrants than the government can process. In 2016, Trump gained ground with Hispanic voters relative to Republicans in 2012, while campaigning on mass deportations for people in the U.S. illegally, winning 28%. That rose to 38% for Trump in 2020, after his harsh immigration policies that included family separation. Diverse Texas districts along the Mexico border, once Democratic strongholds, have shifted toward Republicans.

Cuellar, whose break with liberals on immigration dates back to the Obama era, said the Democratic Party was led astray as Hispanic voters also want to punish lawbreakers.

“That’s a myth,” Cuellar said. “They want border security. Still be respectful of the immigrants, but they want border security.”

He said public perception has moved away from Democrats on the issue — not because the party doesn’t support resources for enforcement, but because “Democrats won’t talk about border security” as much in recent years.

“I’m glad that the White House and other Democrats are looking at this as a very important issue to people — not only people like my constituents on the border but in other places. So yes, I see a shift from the White House, which I support,” he said. “I see a shift from other Democrats, more to the middle, to the center, where most Americans are at.”