South Carolina Sen. Lindsey Graham on Sunday blamed the border crisis on President Obama, but also argued his Republican Party is doomed in the 2016 presidential race unless the GOP House next year helps fix the country’s broken immigration policies.

“I blame Obama for this moment,” Graham told NBC’s “Meet the Press.” If Congress doesn’t pass immigration-reform legislation in 2015 “our chances in 2016 are very low. The House should lead.”

Graham also said that 2008 immigration laws must be changed before he supports Obama’s recent request to Congress for an additional $3.7 billion to help with the crisis at the U.S.-Mexico border, where tens of thousands of Central American children and others have crossed into the United States in recent months with hopes of fleeing widespread poverty and violence.

The law, intended to curb human trafficking, prevents children illegally entering the United States from non-bordering countries from being immediately sent home.

The Republican-controlled House has already indicated its unwillingness to agree to the additional spending.

The Democrat-controlled Senate last year passed comprehensive immigration reform, but such legislation has stalled in the lower chamber.

Graham’s comments followed those made earlier on “Fox News Sunday’ by Texas GOP Sen. Ted Cruz, who largely pinned the border crisis on Obama’s 2012 executive memo. And he escalated Democrats and Republicans blaming each other for making the Central American children victims in the ordeal.

“The cause of this crisis is the promise of amnesty,” he told “Fox News Sunday.”

Cruz argued the number of children trying to enter the U.S. illegally has “skyrocketed” since 2012 when Obama allowed some young illegal immigrants to be eligible for delay deportation.

He says roughly 6,000 children were apprehended in 2011 coming into the U.S. illegally, compared to an estimated 90,000 coming this year and 145,000 in 2015.

Last week, Senate Majority Leader Harry Reid dismissed GOP-led arguments that immigration reform must begin with securing U.S. borders and said that “radical Republicans would rather hold these kids ransom,” then consider reasonable solutions.

Cruz said Sunday that the way to help the children is to "eliminate the magnet, which is President Obama's amnesty."

“President Obama and Harry Reid are both engaging in debates divorced from the facts and reality,” Cruz said. “Harry Reid lives in the Ritz-Carlton in Washington, D.C. And I'm sure from his perspective the border seems secure.”