WASHINGTON (AP) — Democratic leaders in the House proposed somewhat tighter requirements for the care of unaccompanied refugee children as they sought to pass a $4.5 billion emergency funding bill to address the humanitarian crisis involving the thousands of migrant families detained after crossing the U.S.-Mexico border.

Lawmakers and aides said the concessions — and a full court press by top leaders such as Speaker Nancy Pelosi, D-Calif. — were likely to result in a winning tally when the measure comes to a vote later on Tuesday, despite lingering reservations among Hispanic and liberal Democrats.

The Senate hopes to vote on a different, and bipartisan, companion measure as early as Tuesday as the chambers race to wrap up the must-do legislation by the end of the week. Many House Democrats say the Senate version's provisions aimed at helping migrant children are not strong enough. House Democrats seeking changes met late Monday with Pelosi, and lawmakers emerging from a morning caucus meeting were supportive of the legislation.

Rep. Darren Soto, D-Fla., said the Democratic measure would fully fund migrant care and "make sure that we are treating these immigrant children with dignity like any other great country would."

The White House is threatening to veto the House bill, saying the measure would hamstring the administration's border security efforts and raising fresh questions about the legislation's fate.

Changes unveiled Tuesday would require the Department of Homeland Security to establish new standards for care of unaccompanied immigrant children and a plan for ensuring adequate translators to assist migrants in their dealings with law enforcement.

Many children detained entering the U.S. from Mexico have been held under harsh conditions, and Customs and Border Protection Chief Operating Officer John Sanders told The Associated Press last week that children have died after being in the agency's care. He said Border Patrol stations are holding 15,000 people — more than triple their maximum capacity of 4,000.

Congress plans to leave Washington in a few days for a weeklong July 4 recess. While lawmakers don't want to depart without acting on the legislation for fear of being accused of not responding to humanitarian problems at the border, it seems unlikely that Congress would have time to send a House-Senate compromise to Trump by week's end.

In a letter Monday threatening the veto, White House officials told lawmakers they objected that the House package lacked money for beds the federal Immigration and Customs Enforcement agency needs to let it detain more migrants. Officials also complained in the letter that the bill had no money to toughen border security, including funds for building Trump's proposed border wall.

"We've got lives at stake," said Rep. Tony Cardenas, D-Calif. He said the U.S. has been "the gold standard" for treating refugees fleeing dangerous countries, "and I don't think we should compromise that at all."

The meeting may have helped ease Democratic complaints. Rep. Alexandria Ocasio-Cortez, D-N.Y., told reporters before the meeting that she would oppose the bill but left the door open afterward, saying, "I oppose the situation we're in, but my main goal is to keep kids from dying."

Much of the legislation's money would help care for migrants at a time when federal officials say their agencies have been overwhelmed by the influx of migrants and are running out of funds.

"This is strictly a supplemental that's in response to a humanitarian crisis that is taking place right now," said Rep. Lucille Roybal-Allard, D-Calif., one of the authors of the bill. She said language in the measure limits the use of the funding to "food, clothing, better shelter facilities and so on."

The back-and-forth on the spending measure came as Congress' top Democrats criticized Trump for threatening coast-to-coast deportations of migrants.

Over the weekend, Trump tweeted that he would give Congress two weeks to solve "the Asylum and Loopholes problems" along the border with Mexico. "If not, Deportations start!" he tweeted.

The president had earlier warned that there would soon be a nationwide sweep aimed at "millions" of people living illegally in the U.S., including families. The sweeps were supposed to begin Sunday, but Trump said he postponed them.

Pelosi said the threatened raids were "appalling" when she was asked about them at an immigration event Monday in Queens, New York.

"It is outside the circle of civilized human behavior, just kicking down doors, splitting up families and the rest of that in addition to the injustices that are happening at the border," she said.

On the Senate floor, Minority Leader Chuck Schumer, D-N.Y., described Trump's "chilling, nasty, obnoxious threats" and said the president "seems far more comfortable terrorizing immigrant families" than addressing immigration problems.

"I mean, my God, to threaten separating children from their parents as a bargaining chip? That's the very definition of callousness," Schumer said.

It is not clear exactly what Trump, who has started his 2020 re-election bid, means regarding asylum and loophole changes. He's long been trying to restrict the numbers of people being allowed to enter the U.S. after claiming asylum and impose other restrictions, a path he's followed since he began his quest for president years ago. His threatened deportations came as authorities have been overwhelmed by a huge increase of migrants crossing the border into the U.S. in recent months.

For years, Democrats and Republicans have unable to find middle ground on immigration that can pass Congress. It seems unlikely they will suddenly find a solution within two weeks.

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AP Congressional Correspondent Lisa Mascaro and Associated Press writers Andrew Taylor and Colleen Long contributed to this report.