Sen. Lindsey Graham said Sunday that he would help the White House convince his fellow Republicans to support closing Guantanamo Bay if President Obama reverses course and sends the alleged Sept. 11 mastermind and his co-conspirators to military tribunals. 

The South Carolina Republican is considered to be a key player in the administration's strategy to close the detainee camp at Guantanamo. He supports shuttering the facility but opposes trying the alleged architects of the Sept. 11, 2001, terror attacks in civilian court. 

He acknowledged Sunday that he's willing to play ball with the White House on Guantanamo, provided it gives him what he wants on the terror trials. 

"I don't believe Khalid Sheikh Mohammed robbed a liquor store. He's the mastermind of 9/11. ... If he's not an enemy combatant, who would be?" Graham told CBS' "Face the Nation." 

He suggested that using the tribunals for such high-profile terror suspects would go a long way toward easing opposition from the right to closing Guantanamo and sending its detainees to U.S. soil. 

"I can't do it by myself. But I think if we could get Khalid Sheikh Mohammed and his co-conspirators of 9/11 back in the military commission, it would go down well with the public," Graham said. 

Congress has barred the transfer of prisoners who don't have a path to trial -- those who appear to be detained indefinitely -- and refused to give the president the money for a facility to house them on American soil. Meeting resistance, the Obama administration blew by its self-imposed deadline to have the Guantanamo prison closed by January. 

A senior administration official told Fox News the decision on the trials, while "weeks away," is linked to a "basket of other issues" including obtaining congressional funding for a prison to house Guantanamo detainees in Thomson, Ill., and for other terror trials in federal civilian courts. 

Though the goal in reconsidering the trial venue may be in the interest of the president's longer-standing goal of closing Guantanamo, some on the left have reacted fiercely to the prospect. 

The American Civil Liberties Union ran a full-page ad Sunday in The New York Times slamming the president. 

"What will it be Mr. President?" the ad asks in boldfaced type. "Change or more of the Same?" 

In the middle of those words are four photos that show Obama's face morphing into the image of former President George W. Bush. 

But Sen. Evan Bayh, a moderate Indiana Democrat who does not plan to run for re-election, described any concession on the terror trials as part of a worthy compromise. 

"(Obama) is trying to stake out a common middle ground and he gets kicked in the shins by the far left," Bayh told Fox News. 

He told "Face the Nation" that he would be willing to support terror trials in the military tribunal setting. 

"I think the administration gets something, and yet the public gets reassured," Bayh said. "If they want to make progress in the war of ideas by eventually closing down Gitmo, they're going to have to give a little bit on that. ... And that's why I think we have got to find some common ground on this thing." 

Fox News' Caroline Shively contributed to this report.