House Speaker Nancy Pelosi on Thursday downgraded her ante on border wall money from $1 to zero dollars, putting chances for a homeland security spending deal even further out of reach.

President Trump, speaking to reporters at the White House, said Mrs. Pelosi will eventually end up clamoring for a wall when she sees the coming caravans of immigrants, including one with 12,000 people, arrive at the U.S.-Mexico border.

But he also said he’s resigned to the failure of the negotiations on Capitol Hill, where lawmakers are trying to hash out a deal on homeland security spending, with the most prominent sticking point being the president’s $5.7 billion border wall request.

“I don’t think they’re going to make a deal,” he said. “I don’t expect much coming out of this committee.”

The negotiators held their first meeting Wednesday, where Democrats teased their border security counteroffer.

They released an outline Thursday, detailing a plan to cut enforcement against illegal immigration on both the border and interior, and instead pump money into drug interdiction.

The plan would slash the number of detention beds used to hold immigrants who were attempting to illegally cross the border that can be held for deportation from about 45,000 a day now down to about 35,000.

It would also propose limiting the number of people who can be arrested and held from the interior of the U.S., and it would end the detention of immigrant families altogether by 2020.

It would add more agents to U.S. Immigration and Customs Enforcement, though Democrats said they would be used for drug, gang and financial investigations. Democrats’ plan would also add more personnel at border crossings, though it would not grant Mr. Trump’s demand for more Border Patrol agents.

That was still too much for some of the House’s most liberal members and left-wing activist groups, who said they expect Democrats, now in power in the House, to cut immigration enforcement even deeper.

“With 15,000 children locked in cages right now, deaths in detention camps, families being ripped apart every day and the eyes of the world watching for leadership, this ‘not as bad as the Republican plan’s malpractice,’” said Cristina Jimenez, Executive Director and Cofounder of United We Dream.

She said Democrats have for years voted in favor of spending bills that boosted border security and immigration enforcement, and she said it’s time to reverse that and begin to cut from ICE and U.S. Customs and Border Protection.

She complained in particular about Democrats’ plans to boost the number of ICE agents at Homeland Security Investigations — even with the restrictions Democrats included.

Overall, the Democratic plan would boost ICE funding by $369 million over last year, to $7.4 billion, and boost CBP by $278 million, to $14.3 billion.

That CBP number includes hundreds of millions of dollars for new drug-scanning technology, but it cuts even the $1.3 billion that last year’s bill included for border fencing — money that most Democrats voted for at the time.

Mrs. Pelosi, who last month had said she would accept $1 in border wall money, said Thursday that she won’t allow any funding at all.

“There’s not going to be any wall money in the legislation,” Mrs. Pelosi told reporters at her weekly press conference.

She did, though, say she could be open to more barriers of some sort, including “Normandy” barriers. She made an “X” gesture with her hands to show reporters what she meant by that type of barrier.

“If the president wants to call that a wall, he can call it a wall,” she said. “Is there a place where enhanced fencing, Normandy fencing, would work? Let them have that discussion.”

At the White House, Mr. Trump, who over the last few weeks had said what he wanted wasn’t necessarily a wall but rather fencing — the same type that Democrats have voted for repeatedly in the past — said Thursday he’s back to a wall.

“Lets just call them WALLS from now on and stop playing politics,” he tweeted. “A WALL is a WALL!”

• Stephen Dinan and Gabriella Muñoz contributed to this article.

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