Sen. Lindsey Graham (R-S.C.) took aim at President Barack Obama on Sunday, questioning the administration’s national security strategy and charging that a key White House adviser is unfit for the job.

Graham contended in a television interview on “Fox News Sunday” that he is willing to meet Obama more than halfway on national security issues, but he said the White House needs to change course on the way it handles alleged terrorists such as Christmas Day bombing suspect Umar Farouk Abdulmutallab.

Graham also said that Obama’s deputy national security adviser, John Brennan, is the wrong man for the job.

“He has lost my confidence,” Graham said. “I think it’d be better to have a new person in that job.”

In two television interviews, Brennan’s boss, White House National Security Adviser James Jones, defended Brennan and Obama’s strategy against Republican criticism. Jones, appearing on “Fox News Sunday” and CNN’s “State of the Union,” also made a point of emphasizing that the White House has closely consulted with Congress on national security.

“We believe, in the national security council, that national security is not a partisan issue. We consult with both sides of the Hill, we engage with both sides of the Hill,” Jones said on Fox, adding on CNN: “We consult with both sides equally.”

Graham was critical of Brennan’s recent comments about the number of terror suspects who have been freed and then returned to plotting terror acts. He said military law should prevail and that suspects such as Abdulmutallab should not be given Miranda rights.

“Is it any way to fight a war to read Miranda rights?” Graham said. “I think really these policies are ill-conceived, and they need to start over.”

Jones countered that he has studied the issue and the Abdulmutallab case in particular and concluded that the situation was handled properly. Jones said reading the alleged Christmas Day bomber his Miranda rights has not prevented law enforcement from obtaining information from the suspect that is critical to national security — either before or after he lawyered up.

“We’ve had a long record of prosecuting terrorists in federal courts with great success,” Jones said on CNN. “The best advice will come from the attorney general’s office, and we’ll make a decision.”

Graham said that he is willing to work with Obama on finding a path to closing the military prison at Guantánamo Bay, Cuba. As for the situation in Iran, Graham said that the “U.N. is letting the world down. … So I support the coalition of the willing, but at the end of the day, I want behavior to change.”

When it comes to dealing with Iran, Jones offered, the United Nations is “our first step,” but he said the Obama administration would not rule out other options.

“I think we will get tough as quickly as possible,” Jones said on “Fox News Sunday.”

The administration supports democracy in Iran, Jones said, but made clear that “we are not actively engineering regime change.” However, he said the “very tough sanctions” the administration backs could lead to regime change.

Graham said that if Obama is willing to retool his priorities and strategies, then bipartisanship will be possible. “If the president is willing to change course on these major issues, then he will get bipartisan support,” Graham said, adding, “We’re all in this together.”

“I think we need to stop all this fighting among ourselves and direct our fight at our enemies,” Graham said.

“Our national security is not a partisan issue,” Jones added.