Sen. Lindsey Graham (R-S.C.) said Thursday that he no longer favors closing the terrorist detention center maintained by the U.S. at Guantánamo Bay, Cuba.

Graham, who'd previously sought to work with the Obama administration to close the prison, said there's "no way" to close the facility at this point.

"There's no way to close Gitmo now," Graham said Thursday on Laura Ingraham's radio show when asked if he still favors closing Guantánamo.

"I'm being honest. Quite frankly, it doesn't matter to me where you house these people; it matters what you do with them," he added.

That's a shift for Graham, who had previously hoped to close the prison, which he regarded as a public relations disaster for the United States.

"Gitmo itself is a well-run prison, but I believe it continues to be a problem in the greater war effort," the South Carolina senator said in a March appearance on Fox News.

Graham said Thursday that he favors prosecuting those prisoners on-site.

"Gitmo is a place with a viable courtroom," he said. "Let's use them."

President Obama had ordered that the facility be closed shortly after taking office in January of 2009. But almost two years since then, the administration hasn't been able to overcome political opposition to moving the alleged terrorists detained in Cuba to any other location.

For Graham, his shift also represents some of the tough political realities he personally faces. Conservatives who have been unhappy with his efforts to partner with Democrats on issues like immigration and energy-and-climate legislation have threatened him with a GOP primary challenge when he's up for reelection in 2014.

Update, Fri., Dec. 3 at 9:36 a.m.: A spokesman for Graham says the senator still favors closing the military prison at Guantanamo. "Like former President Bush and others, Senator Graham still supports closing Guantanamo.  He made it clear from the start that there was only one way to close the facility and that was to do it in a national security-centric manner.  And it is on that front that the Obama Administration has fallen far short of the mark," said Kevin Bishop, a spokesman for Graham.