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House Speaker John A. Boehner, Ohio Republican, set up the task force after rejecting Mr. Obama’s $3.7 billion request, which was widely criticized as excessive and has no chance of surviving intact.

Senate Democrats also are preparing to slash Mr. Obama’s spending request.

Senate Appropriations Committee Chairwoman Barbara A. Mikulski, Maryland Democrat, is scheduled to release an alternative package Wednesday that would trim $1 billion from Mr. Obama’s request. It also would shift $225 million to Israel’s Iron Dome missile defense system for its battle again Hamas militants in Gaza and $615 million to Western states responding to wildfires.

Lawmakers must finalize the bills and reconcile any differences between the chambers’ versions in less than two weeks, when Congress is scheduled to adjourn for its August recess.

The House task force’s emphasis on border security measures should help win support among conservatives, who have demanded that the administration seal the border before addressing other immigration issues.

The Obama administration is looking for facilities to shelter the children, who have been transported as far as Chicago and Virginia, while officials attempt to reunite them with relatives in the United States.

“Republicans have made clear that we support efforts to take care of these children, return them safely to families in their home countries and secure the border,” Mr. Boehner said Tuesday as he called on the president seek a bipartisan solution.

“The lack of leadership from this White House, and President Obama’s refusal to stand up to critics in his own political party, are jeopardizing our ability to find common ground and help the kids who are caught in the middle of this crisis,” he said.

Revisiting a 2008 law

The task force will recommend changing a 2008 law that delays immigration hearings for children from Central America, which is home to most of the 57,000 unaccompanied children who have arrived illegally so far this year.

The 2008 law, known as the William Wilberforce Trafficking Victims Protection Reauthorization Act, was intended to protect Central American children from human trafficking, but critics say it has become a foothold and incentive for Central American children to reach the U.S.

At least 90,000 children will be caught this year and more than 140,000 next year, according to a U.S. Customs and Border Protection memo.

Until recently, about 8,000 unaccompanied children per year attempted to cross the border.

Mr. Obama and House Minority Leader Nancy Pelosi, California Democrat, previously supported changing the law but reversed their positions after vocal opposition from the Congressional Hispanic Caucus.

The Republican recommendations, particularly changes to a 2008 law that delays deportations of children from Central America, will face stiff resistance from the White House and congressional Democrats.

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