Sen. Lindsey Graham Lindsey Olin GrahamMcConnell locks down key GOP votes in Supreme Court fight Will Republicans' rank hypocrisy hinder their rush to replace Ginsburg? Momentum growing among Republicans for Supreme Court vote before Election Day MORE (R-S.C.) on Sunday said Republicans are partially responsible for not passing comprehensive immigration reform.

“Shame on us as Republicans for having a body that cannot generate a solution to an issue that’s national security, that’s cultural, that’s economic,” Graham said on CNN’s “State of the Union.”

The Senate has passed an immigration bill three times, Graham said, adding that he “loves” his GOP colleagues in the House.

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“I’m close to the people in the House, but I’m disappointed in my party. Are we still the party of 'self-deportation'?” he asked.

President Obama in a separate interview Sunday blamed Speaker John Boehner (R-Ohio) for not taking up legislation the Senate passed in 2013 on immigration and urged Congress to pass a bill on the issue.

“Is it the position of the Republican Party that the 11 million must be driven out? I have never been in that camp as being practical. I am in the camp of securing our borders first, fixing a broken legal immigration, have an E-Verify program so you can't cheat,” Graham added.

Obama has made a “political decision” to issue his own executive actions on immigration, said Graham, who called the new orders unconstitutional.

“He made a political decision to try to divide the Republican Party,” he said, “and take the office of the presidency to a level no one else has gone.”