WASHINGTON — Democrats have consistently derided Donald Trump’s campaign promise to build a “big, beautiful’’ concrete wall spanning the entire US-Mexico border as stupid and wasteful. But with the fate of 700,000 young unauthorized immigrants in the balance, that party line is beginning to fracture.

Some Democrats are wondering if, just maybe, it’s time to give the president something on the border that he can call a wall.

“Look, he’s got to save face,’’ said Representative Henry Cuellar, a Democrat from Texas, whose district includes a swath of the US-Mexico border at the bottom tip of the state.

Cuellar was one of about a dozen lawmakers included in a freewheeling, bipartisan discussion with the president at the White House on Tuesday about how to protect young recipients of an Obama-era program known as DACA, or Deferred Action for Childhood Arrivals. Trump announced in September that the program, which protects certain young people brought to the United States illegally as children, would end unless a compromise could be crafted.

With many DACA recipients becoming eligible for deportation in March, Democrats are pushing for DACA protections to be included in a spending deal that must pass by Jan. 19 to keep the government open.

In the discussion, nearly an hour of which was televised, Trump doubled down on his demand for a wall in exchange for protecting the DACA recipients, also known as Dreamers. But once the cameras left the room, the president showed much more flexibility, according to lawmakers.

“It’s not a 2,000-mile physical wall,’’ said Senator Jeff Flake, a Republican from Arizona. “It’s only 700 or 800 miles total, some of that replacement. And more importantly, the wall is really a fence.’’

With nearly 700 miles of some type of fencing already in place along the border, would Democrats hold out on a DACA deal over a fence — which Trump could call a wall — that mainly replaces existing structures?

It’s unclear. Senate minority leader Chuck Schumer, a Democrat from New York, tweeted Tuesday that Trump’s demand for a “completely ineffective’’ border wall was why they had been unable to reach a deal so far. Yet later that afternoon, Schumer told reporters he believed both sides would be able to reach a border security deal they could “live with.’’

The Trump administration released a proposal earlier this week that demanded $18 billion from Congress for a wall to be built over 10 years.

Representative Ruben Gallego, a Democrat from Arizona and an adamant opponent of Trump’s wall, said he would be willing to consider a border security plan that was limited to replacing existing fencing.

“If he comes back with a solid plan that says these are the 700 miles of replacement fencing I want for already pre-existing walls . . . then we could obviously look at it as long as it’s actually providing real security and not just an ego boost to him and his xenophobic base,’’ Gallego said.

“If Trump gets to declare a victory, that’s fine for me as long as people are protected,’’ Gallego added.

Cuellar, the son of migrant workers who represents South Texas, says some in the Democratic caucus are adamantly opposed to more barriers on the border. But he sees potential compromise with Trump in a “levy wall’’ — mounds of dirt covered in concrete that help prevent flooding. Some stretches of levy wall already exist on the Texas-Mexico border, a part of the approximately 700 miles of barriers currently in place.

“If you let the Border Patrol chiefs work with the local communities, you could probably get some buy-in on some fencing,’’ said Cuellar.

“I think it’s silly to throw money at a 13th-century solution,’’ said Representative Michael Capuano of Massachusetts, referring to Trump’s proposal of a continuous concrete wall. But Capuano said he’d be open to more “thoughtful’’ security proposals, including some fencing.

Yet several Democrats are still pushing for a so-called clean bill. A spokesman for Senator Edward Markey of Massachusetts said the senator “agrees with leader Schumer that any DACA deal should stand on its own’’ and that young DACA recipients should not be used as “pawns’’ to satisfy Trump’s base.

Senator Mazie Hirono of Hawaii told reporters she believes the border security portion of the DACA deal will be the “hardest to negotiate’’ because she is opposed to any type of wall on the border. “The general consensus is that a wall is not necessary,’’ Hirono said.

Lobbyists and activists fighting to protect young immigrants, however, are less concerned with fencing than with making sure Democrats use their leverage on the upcoming spending bill to deliver a deal to protect Dreamers.

Republicans need Democratic votes to fund the government before Jan. 19, though Democratic leadership hasn’t yet directly threatened to withhold their votes if they don’t get what they want on DACA.

“If Congress passes another stop-gap funding bill without protecting Dreamers from deportation, Democrats and Republicans alike will face a massive backlash from the grass roots,’’ said Ben Wikler, the Washington director of the organization MoveOn.

Frank Sharry, executive director of America’s Voice, a pro-immigration advocacy group, said his organization would be unlikely to protest a DACA deal that included replacing existing fencing. He said he could imagine a deal that includes fence repairs and some new infrastructure that allows Democrats to say “there is no money in this for a concrete wall’’ and Trump to say “I got funding to build my wall.’’

Trump’s demand for a wall isn’t the only hurdle to a deal, however. The president also said he wants to end the diversity visa lottery, which grants 50,000 green cards each year to people from countries with low levels of immigration to the United States, and also to curb “chain migration’’ — the president’s term for US citizens’ ability to sponsor their relatives for green cards. It’s also unclear if the deal would cover just the 700,000 young people who currently receive DACA protection or a broader group of 2.1 million unauthorized immigrants brought to the country as children who are eligible for protection under the Dream Act.

House minority whip Representative Steny Hoyer of Maryland told reporters he did not believe the diversity lottery and chain migration should be a part of DACA talks at all.

And even just focusing on DACA recipients when it comes to chain migration, as Trump has proposed, would be controversial among Democrats.

Gallego said limiting DACA recipients’ ability to sponsor relatives once they become US citizens is a “no-go’’ for him, because it would effectively create a second class of citizenship.

“Once you’re a citizen, you should have the full rights of citizenship,’’ Gallego said.

Liz Goodwin can be reached at Liz.Goodwin@globe.com. Follow her on Twitter @lizcgoodwin