Republicans called on President Obama to dispatch National Guard troops to the United States-Mexico border while Congress works out potential fixes to policies some say have contributed to a rash of Central American immigrants arriving through Mexico.

GOP Texas Gov. Rick Perry said that Obama should "pick up the phone" -- a reference to the president's pledge to take action on an array of issues if Congress doesn't -- to send 1,000 National Guard members to the border.

"Here's his opportunity to truly lead," Perry said on "Fox News Sunday".

More than 52,000 children and teenagers have been caught by Border Patrol agents since last October, with many of them are fleeing violent Central American nations wrapped up in the illegal drug trade.

The White House has asked Congress to approve a $3.7 billion package to address the issue, but the House doesn't look likely to approve it. House Homeland Security Committee Chairman Michael McCaul, R-Texas, said the lower chamber might be amenable to a "targeted approach," but that it wouldn't write a "blank check."

The rush of Central American immigrants has overwhelmed the system. They're treated differently than Mexican immigrants under a 2008 law signed by President George W. Bush -- Central American immigrants can see an immigration judge while Mexicans are often quickly bused back across the border.

Republicans blamed that difference, along with a 2012 executive order that allowed children who immigrated to the U.S. before June 2007 to defer deportation, for the immigration spike.

McCaul said the 2008 law needs to be changed to allow quicker deportation.

"We think that law has to be changed," he said on "Fox News Sunday". "You have to send a message of deterrence."

Administration officials have rejected claims that its deportation deferral policy is driving matters, instead pinning the emphasis on crisis-riddled Central American nations pushing people to flee.

"Yes, the immigration laws are being enforced, though we are faced with an extraordinary situation with thousands of people, young people especially, are fleeing Central America for economic reasons, to get away from really endemic violence in their countries," Attorney General Eric Holder said Sunday on ABC's "This Week." "We are surging immigration judges to the border to process people."

Rep. Beto O'Rourke, D-Texas, backed the White House plan, saying Sunday on CNN's "State of the Union" that, "The origin of the problem is this instability and insecurity in Honduras, in Guatemala and El Salvador. And we really won't stop this crisis until we address those core issues."

Rep. Donna Edwards, D-Md., defended the administration's border patrol efforts — a May report from the nonpartisan Congressional Research Service noted apprehensions of illegal immigrants along the Southwest border dropped from 1.6 million to 420,000 between 2000 and 2013.

But apprehensions rebounded to 414,000 in 2013 after hitting a 41-year low of 328,000 n 2011. And the Los Angeles Times reported Sunday that deportations of children under 18 at the border have plummeted since 2008, the final year of Bush's administration, from 8,143 to 1,669 in 2013.

"As tragic and as terrible as this situation is, we cannot have an unending flow of children from all over the world, much less Central America into our country," Sen. John McCain, R-Ariz., said Sunday on CNN's "State of the Union."