Leading Republican lawmakers balked on Sunday at supporting a White House spending request aimed at bolstering the U.S. border with Mexico, where thousands of children have crossed recently, while calling for changes in the law to allow faster deportations.

The White House has asked for $3.7 billion in emergency funds to help pay for border security, temporary detention centers and additional immigration court judges to process asylum cases.

The Obama administration warned lawmakers on Thursday that border security agencies would run out of money this summer if the request was not approved.

Senator John McCain, an Arizona Republican, said when asked about the spending bill that the priority had to be stopping the flow of children and teenagers from Central America to the United States.

"The best way to do that is for planeloads of these young people to be returning to the country of origin," he told CNN's "State of the Union." "As soon as they (parents) see their money is not effective in getting their kids to this country, it will stop."

More than 52,000 children traveling alone from Central America have been caught at the U.S.-Mexico border since October, twice as many as the same period the year before.

U.S. immigration officials say the crisis is being driven by poverty and gang and drug violence in Central America, as well as rumors perpetuated by smugglers that children who reach the U.S. border will be permitted to stay.

House of Representatives Appropriations Committee Chairman Harold Rogers said last week that the Obama administration asked for "too much money" but declined to say what an appropriate figure would be.

Representative Michael McCaul, a Texas Republican, also declined to support the spending bill. "We're not going to write a blank check for over $4 billion," he told "Fox News Sunday." McCaul is chairman of the House Homeland Security Committee.

McCaul said he would support changing a 2008 law that requires deportation proceedings for children that arrive from countries that do not share a border with the United States. This would allow authorities to quickly deport newly arrived Central American children, as they do Mexican children.

McCaul said that bill could see action this summer.

"It's a very tragic human crisis at the border, none like I've ever seen before. I think we have to act before the August recess," he said.

The bill saw opposition from one Democrat, Representative Joaquin Castro of Texas.

"That 2008 law, passed under George W. Bush, was passed for a reason," he told NBC's "Meet the Press." "Many people believe that these kids should have a chance to make their case for asylum. So I think we've got to be careful when we consider completely doing away with that law."

Texas Governor Rick Perry pressed the White House to send National Guard troops to the border to aid the border patrol, which has been stretched thin by the mass influx of minors.

"They need to be right there on the river because that's the message that gets back to Central America. It's important to do that because this flood of children is pulling the border patrol away from their normal duty of keeping bad people (out)," he told "Fox News Sunday."

Perry also said that conversations among Central Americans had been monitored.

"We listen to the conversations. Er, I should say that, the conversations are being monitored with calls back to Central America and the message is, 'Hey, c'mon up here. Everything is great. They're taking care of us,'" he said.