HENDERSON, Nev. >> President Barack Obama is shrugging off Republican criticism of his actions to lift the threat of deportation from millions of immigrants living illegally in the United States.

In an interview broadcast Sunday on ABC’s “This Week,” Obama said it was important that he act unilaterally to prioritize the deportation of criminals and recent arrivals and spare those who have lived here illegally for at least five years and have roots, including children who are American citizens.

“Why we would prefer a system in which they’re in the shadows, potentially taking advantage of living here but not contributing?” Obama said in the interview, which was taped Friday in Las Vegas after Obama delivered an immigration speech there.

The president pointed to executive orders issued by Democratic and Republican predecessors and said presidents exercise “prosecutorial discretion all the time.”

Obama’s executive actions, which he announced Thursday, have drawn a withering response from Republicans, but also has laid bare divisions within the GOP over how to deal with immigration.

Sen. Ted Cruz, R-Texas, rejected Obama’s claim of prosecutorial discretion. “Essentially he’s gotten in the job of counterfeiting immigration papers, because there’s no legal authority to do what he’s doing,” Cruz said on “Fox News Sunday.”

A second Republican, Sen. Lindsey Graham of South Carolina, said his party shares the blame for failing to get an immigration bill through the House of Representatives.

“Shame on us as Republicans for having a body that cannot generate a solution to an issue that is national security, it’s cultural and it’s economic. The Senate has done this three times,” Graham said on CNN’s “State of the Union.”

Indeed, Obama cast his decision as the result of the Republican-led House’s failure to act on a comprehensive immigration bill the Senate passed with bipartisan support in June 2013, or advance legislation of its own.

He said Republicans still could pass an immigration bill.

Rep. Raul Labrador, R-Idaho, said he had pressed the Republican leadership to start passing legislation two weeks ago on the immigration issue.

“We are going to pass legislation, but it is not going to be the legislation the president is asking for,” Labrador said. “We as Republicans don’t believe you should give amnesty first and talk about security later, which is what the Senate bill did.” Labrador spoke on “Face the Nation” on CBS.

Obama spent the weekend in Nevada, mostly playing golf, after the speech and was returning to the White House on Sunday evening.