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A Republican working group dedicated to addressing the influx of unaccompanied migrant children has released its recommendations on how to deal with the situation at the nation’s southern border.

The group, led by Rep. Kay Granger of Texas, recommends that the U.S. should deploy National Guard troops to the border, aim to process families apprehended at the border within one week, and amend a 2008 law that requires additional legal processing for children from Central America.

"Without trying to fix the problem, I don’t know how we are actually in a position to give the president any more money."

The 2008 law is a major sticking point in negotiations between both parties and both chambers of Congress; many Democrats say a rolling back of the measure would result in children being deported back into unsafe environments, while Republicans – and the Obama administration -- suggest that a change is needed to speed the processing of detainees and to disincentivize parents from sending their children to the U.S. illegally.

Speaking to reporters on Wednesday, House Speaker John Boehner would not commit to a vote on the proposal before Congress adjourns for its August recess, saying only that he is "hopeful" that Congress will act.

Boehner also reiterated that changes to the 2008 law should be tied to any funding request.

"Without trying to fix the problem, I don’t know how we are actually in a position to give the president any more money," he said.

In this July 12, 2014, photo, Central American migrants ride a freight train during their journey toward the U.S.-Mexico border in Ixtepec, Mexico. The number of family units and unaccompanied children arrested by Border Patrol in the Rio Grande Valley has doubled in the first nine months of this fiscal year compared to the same period last year. (AP Photo/Eduardo Verdugo)Eduardo Verdugo / AP

The Republicans’ proposal also includes additional funding for immigration judges and “aggressive messaging campaigns” in the Central American countries from which migrants are fleeing violence and poverty.

The group’s recommendations now will go the House Appropriations Committee, which will work on drafting a bill.

Stressing that there is no legislation yet, an aide on that committee says the proposal’s cost could be as low as $1.5 billion for the rest of this calendar year.

That’s far less than the $3.7 billion originally requested by the Obama administration to deal with the issue.

A separate piece of legislation is also being readied in the Democratically-controlled Senate. The price tag on that bill, which is set to be considered in the coming days, totals $2.7 billion.

But it's unclear whether both parties and chambers of Congress can resolve conflicts between the dueling border bills.