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The administration has also promised to add more judges to courts in the southwest so immigrants’ claims can be processed faster and they can be deported, if need be. And the Department of Homeland Security is adding 700 more beds to hold illegal immigrant families. Currently, the department has fewer than 100.

That surge in resources has angered immigrant-rights groups, who say it is inhumane.

Some activists plan a rally Thursday outside the Mexican consulate in Los Angeles to urge that country not to stiffen its own security to prevent migrants from crossing, while another group plans an event near the White House next week to try to pressure Mr. Obama.

Even with the new resources, the administration is still falling short. It doesn’t even have the space to house all of the children. The military announced earlier this week that the several thousand beds it made available on military bases are full.

Local communities have torpedoed a number of other locations where the government had wanted to warehouse the children.

On Wednesday, Rep. Lou Barletta, Pennsylvania Republican, said he had been informed that the Department of Health and Human Services, which takes the children after they are processed by Homeland Security, won’t look for a facility in Pennsylvania.

“This problem has not ended because one group has taken one town or state off its list,” Mr. Barletta said. “This is an ongoing problem — with ongoing consequences — and it was foreseeable and preventable.”

He and other Republicans say the surge in children and families can be traced back to Mr. Obama’s nondeportation policies, which include granting tentative legal status to hundreds of thousands of young adult illegal immigrants and generally halting the danger of deportation for most illegal immigrants in the interior.

But Democrats counter that if House Republicans would take up and pass the Senate bill legalizing illegal immigrants, it could help solve the surge.

“That is because the Senate bill greatly enhances border protection while setting up clear and fair rules for immigrants,” said Sen. Barbara Boxer, California Democrat.

The Senate bill included tens of billions of dollars to double the number of Border Patrol agents to 40,000 and add technology and more fencing. But that border security proved so controversial at the time that when House Democrats wrote their own bill, they dropped all such provisions.