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Rep. Raul M. Grijalva, Arizona Democrat, said Thursday that keeping the 2008 law in place is “the fundamental line in the sand for many of us.”

“We feel that the law is there for a reason — that the due process involved in this law requires that these children have advocates, that they have an opportunity to have someone represent them,” Mr. Grijalva said on C-SPAN’s “Washington Journal.” “How is a 5-year-old child from Honduras going to be able to make a claim of either asylum or fear of violence?”

The White House said changes to the law should proceed slowly and separately from the funding proposal. The administration is struggling to adhere to requirements for housing the youths and reuniting them with relatives in the U.S.

Republicans are skeptical of the Democrats’ preferred scenario.

“I want to be clear: There’s going to be no blank check for the president and his allies,” House Speaker John A. Boehner, Ohio Republican, said at his weekly press conference at the Capitol.

“Some in Washington may view every new crisis as an opportunity to demand more taxpayer dollars, but the American people don’t see it that way. They want solutions,” he said. “And I’m still hopeful that common ground can be found.”

At a forum hosted by the Center for Strategic and International Studies, Mr. Hernandez and Mr. Perez said U.S. foreign policy was driving their citizens northward.

Mr. Perez said U.S. efforts to combat drug gangs in Colombia and Mexico are pushing organized crime into Central America. “What has been good for Colombia and Mexico has been bad for us,” he said.

Mr. Hernandez said the drug trade — “the monster” — thrives off of Americans’ appetite for illegal drugs. “That monster has one foot in Central America and one foot in the U.S.,” he said.

The Obama administration also has blamed violence and drug gangs in Central America for forcing families and children to flee to the U.S.

Republicans, however, say Mr. Obama’s easing of deportations and other immigrant-friendly policies are encouraging border jumpers.

“These kids were here in this country at the invitation of the president,” said Sen. James M. Inhofe, Oklahoma Republican. “I think everyone knows it. Nobody says it.

“All of them were programmed to say they have relatives here, they were invited to come up here, they’re going to stay here,” Mr. Inhofe said on MSNBC’s “The Daily Rundown.” “At the same time, HHS says we’re not going to send them back. As long as they have that assurance, more are coming in.”

Mr. Perez and Mr. Hernandez suggested that more U.S. aid to their countries would help solve the problem.

“We’re dealing with the problem, even with our limited means,” said Mr. Hernandez. “But with the level of complexity of the problem … we can’t do it alone.”

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