Immigrants who have been caught crossing the border illegally are housed inside the McAllen Border Patrol Station in McAllen, Texas where they are processed on Tuesday, July 15, 2014. (Rick Loomis/AP)

The influx of migrants attempting to cross the U.S.-Mexico border has slowed in recent weeks, administration officials told lawmakers Wednesday.

The ebb of migrations into the country came as a growing number of congressional Democrats are opposed to weakening legal protections for young children crossing the U.S.-Mexico border from Central America, making it less likely that Congress can agree on a deal to address the crisis before lawmakers leave Washington for a five-week summer recess.

The issue is a flash point in the debate over how to stem a tide of tens of thousands of unaccompanied minors coming into the United States, primarily from El Salvador, Guatemala and Honduras. A 2008 law grants extra protections to youths from those countries compared with Mexico or Canada, making it more difficult to deport them quickly.

As the Obama administration seeks to win passage of $3.7 billion in emergency funding to handle the influx, Republicans and some Democrats have said they cannot support authorizing more money to deal with the crisis unless it is coupled with changes in current policy to speed up deportations.

View Graphic Public chastises both Obama and Republicans on immigration wave

But House Minority Leader Nancy Pelosi (D-Calif.) and members of the Congressional Hispanic Caucus — a key bloc on immigration issues — came together Wednesday to oppose the idea. The growing opposition among Democrats will make it more difficult for the GOP-led House and the Democratic-run Senate to reach an accord before Congress leaves Aug. 1 for its annual summer break.

Members of the Hispanic caucus personally conveyed their opposition to changing current deportation policy during a closed-door White House meeting with Obama on Wednesday.

“We had an emotional meeting, but emotional in the sense that we were connected,” Rep. Luis Gutierrez (D-Ill.) told reporters afterward. “We asked him to be our champion, we asked him to be a hero to our community, and he responded to us as a champion and as a hero, in my opinion.”

During the meeting Obama told the group that he wanted “to find a way to ensure due process but also speed things up” in the processing of young migrants, according to another lawmaker in the room who asked not to be identified in order to frankly describe the president’s opinions.

Pelosi told the New York Times in an interview Wednesday that using Obama’s request for more money to change how the federal government deals with young migrants would be “exactly the wrong way to go.” She added, “Is the only immigration bill we’re going to have one that hurts children?”

During an interview with The Washington Post on Tuesday, Pelosi also derided Republicans for “slow-walking” proposals to address immigration reform and the border influx.

“This is the most tragic thing. It’s a humanitarian crisis: The bishops, the U.N., the pope has even spoken out,” she said. “But these guys, they’re doing politics on little children at the border.”

At least 57,000 children have crossed illegally into the country this year, according to government statistics, a figure that far exceeds totals from recent years. During a closed-door meeting for senators Wednesday, Homeland Security Secretary Jeh Johnson and other officials said that apprehensions of illegal border crossers has dropped over the past three weeks to an average of 700 per day, down from 1,600.

Sen. Thomas R. Carper (D-Del.), who chairs the Senate Homeland Security and Governmental Affairs Committee, said that officials told senators that on one day last week, about half of the migrants apprehended were male, roughly a quarter were adults with children and 1 in 7 were unaccompanied minors.

Officials also said that caring for young migrants still in the custody of federal agencies is costing an average of $200 per child per day, according to Sen. Marco Rubio (R-Fla.).

“The whole room, you could hear the murmuring about the costs associated with this,” Rubio told reporters. “We’re a compassionate country. We’re going to treat people who come here in a humane way, but I think now we’re starting to see the human cost and the economic costs of providing care for those who’ve entered the country illegally, and it behooves us to address this as quickly as possible.”

Rep. Joaquin Castro (D-Tex.) said any change in policy “short-circuits due process for the children.” The feelings of the Hispanic Caucus is where “a lot of Americans are,” he said. “They feel that the kids should have their day in court, should have the right to fight for asylum.”

At the daily briefing Wednesday, White House press secretary Josh Earnest declined to comment on Democratic opposition but said, “Our position is that we would like to see Congress grant additional authority to the Secretary of Homeland Security so that he could exercise his own discretion, to enforce the law more efficiently.”

When it came to congressional action on the border crisis, Earnest said that “funding is the priority.”

A narrow 53 percent of respondents to a Washington Post-ABC News poll published this week support Obama’s request for emergency funding and to speed up deportations, but its prospects in Congress remain murky.

In the House, aides said a Republican “working group” studying border issues was nearing completion on a set of proposals for House Speaker John A. Boehner (R-Ohio) and his leadership team to review. Rep. Kay Granger (R-Tex.), who leads the group, told reporters that she hopes the House will take up the issue by the end of the month.

Sen. John McCain (R-Ariz.) told reporters that he met with Boehner Wednesday to discuss border issues and that House GOP leaders understand that they must address the crisis in the coming weeks.

“They know that it’s important that we not go out for August without acting,” he said. “We can’t let that happen.”

David Nakamura contributed to this report.