Otto Perez Molina, president of Guatemala, says his government is prepared to accept citizens sent home and suggests that more funding for U.S.-Mexico border security may be shortsighted. (Jeff Simon, Ed O'Keefe, Marlon Correa and Randy Smith/The Washington Post)

President Obama told Central American leaders Friday that his administration would return children who are here illegally to their home countries, but a substantive U.S. response to the border crisis seemed to grow more remote amid deepening political divisions in Washington.

House Republicans dramatically slashed the amount of emergency money they are willing to devote to dealing with the tens of thousands of unaccompanied minors who have arrived at the U.S.-Mexico border, lessening chances for an ambitious pact before lawmakers leave Washington for their summer break.

The setback undercut the administration’s bid to mount an aggressive push to stem the flow of illegal immigration and raised doubts about Washington’s ability to restore order in the Rio Grande Valley, where U.S. border patrol stations have been overwhelmed by the influx. More than 57,000 children and an additional 55,000 parents with children have been apprehended this year.

Senior administration officials acknowledged that there was little hope inside the West Wing that Congress would strike a quick deal over Obama’s request for $3.7 billion in emergency funding to deal with the crisis. Obama’s meeting with the presidents of Guatemala, Honduras and El Salvador at the White House was intended to send a stern message to those countries to stop the immigrant flow, but the president also used a brief appearance before reporters to urge action from his GOP critics. “It is my hope that Speaker [John] Boehner and House Republicans will not leave town for the month of August for their vacations without doing something to help solve this problem,” Obama said in the Cabinet Room. “There have been a lot of press conferences about this. We need action.”

But after a private meeting, House Republicans said they would reduce their own emergency funding proposal to $1 billion, a third less than what GOP leaders proposed earlier this week. The move was viewed as an effort to placate conservatives who have been reluctant to support a large spending plan with just two months left in the fiscal year.

Dangerous journeys taken by unaccompanied children

The shrinkage underscores the challenge facing Boehner (R-Ohio) as he rushes to reach a consensus on a package that could pass the House with near-majority Republican support before adjournment Friday.

Boehner is now gambling that he can win passage next week by lowering the overall cost and including provisions to amend a 2008 anti-trafficking law to reduce legal protections for Central American minors.

After consulting with colleagues in recent days, Rep. Kay Granger (R-Tex.), who led a House working group on immigration, said Friday that Republicans are down to “bare-bones suggestions.”

Other GOP members closely watching the process said that Boehner may have no choice but to reach across the aisle for Democratic support to win approval for a funding package.

“John is going to lose 60 Republicans no matter what he does,” said Sen. Lindsey O. Graham (R-S.C.), a Boehner ally. “Sixty Republicans are ready to vote against anything, so he may have to find some Democrats to vote with him.”

At the White House, press secretary Josh Earnest was cynical about Republicans’ willingness to address the problem. “What we’ve seen from Congress is a lot of talk but not really any action,” Earnest said. “It is an indication that they’re not willing to live up to their own rhetoric when it comes to dealing with this issue.”

Senate Democrats, meanwhile, are working on their own proposal, which would spend $2.7 billion to provide more resources at the southern border. But their proposal will not include changes to the 2008 law, which many Democrats oppose changing.

The Central American leaders said they agreed with Obama that the crisis is a shared responsibility between all four of the countries, as well as Mexico. But they also used their time before Obama to make the case for more U.S. economic aid to deal with the violence and poverty in some regions of their countries. They argued that the problems at home, caused by violence and poverty, have helped spur the migration north.

In response to a question from a reporter, Obama confirmed that his administration is considering a plan to set up a U.S.-run program in Honduras that would allow locals to apply for refu­gee status in the United States without leaving the country. But the president emphasized that there would be narrow requirements.

“It would be better for them to apply in-country rather than take a very dangerous journey up to Texas to make those same claims,” he said. “But I think it’s important to recognize that would not necessarily accommodate a large number of additional migrants.”

Obama also delivered a blunt warning that most of the children who have already arrived in the United States “will at some point be subject to repatriation to their home countries.”

But the Central American leaders warned that Washington should not be in a hurry to send back all of the children: Many have fled dangerous areas and have parents already living in the United States.

Honduran President Juan Orlando Hernández, who studied at the State University of New York, in Albany, said he wished that his wife and daughter would have been able to join him in the United States during that time. He said he empathized with those Central American parents who live here and summoned their children north to join them.

“This is a question of humanity,” Hernández said, standing in front of the West Wing after his meeting with Obama. “If their parents are here, it’s the principle — the primary interest of the child.”

Robert Costa and Paul Kane contributed to this report.