The No.2 Republican in the Senate took President Obama to task Sunday for claiming Guantanamo Bay created more terrorists than it ever detained by serving as a recruiting tool for Al Qaeda. 

Sen. Jon Kyl, R-Ariz., called the charge "palpably false" and said the White House has not provided any evidence to back up the claim. 

"He meant to say that 770 people or more became terrorists because we have a prison at Guantanamo?" Kyl said on "FOX News Sunday." 

"9/11 hijackers didn't do their deeds because of Gitmo. The people who ... blew up the (U.S.S.) Cole or the Kolbar Towers or the first World Trade Center didn't say, 'There's Gitmo down there,' because it didn't exist. And even after that I don't think you saw guys sitting around in some coffee shop in Saudi Arabia, saying, 'You know, those Americans have this prison called Gitmo, I think I'll become a terrorist,'" he said. "I mean, it's palpably false to suggest that the existence of Gitmo created terrorism, and yet the president gets away with that." 

Republicans have exploited tensions and concerns among Democrats, and their constituents, over where the Guantanamo detainees will eventually be transferred should Obama follow through on his plan to close the prison by January 2010. Kyl's comments hammered the GOP theme that closing Guantanamo is not as inevitable or necessary as the administration makes it out to be. 

In somewhat of a coup for the minority party, the Senate joined the House last week in pulling funding for the closure of the facility, by a vote of 90-6, pending a plan from the administration. 

Obama delivered a speech on Thursday meant to calm those concerns and stress the need to close the prison, for the betterment of national security and America's image. 

In the address, he said the prison set back America's "moral authority" in the world and stoked extremism. 

"Meanwhile, instead of serving as a tool to counter terrorism, Guantanamo became a symbol that helped Al Qaeda recruit terrorists to its cause. Indeed, the existence of Guantanamo likely created more terrorists around the world than it ever detained," Obama said. "It is a rallying cry for our enemies. ... By any measure, the cost of keeping it open far exceed the complications involved in closing it." 

In questioning that claim, Kyl also echoed some of the concerns expressed by former Vice President Dick Cheney, who delivered a competing speech Thursday on national security. 

"We haven't done anything wrong there," Kyl said. "We haven't lost our values and Dick Cheney's exactly right in what he said in his speech." 

But the Obama administration and congressional Democrats continue to claim that Guantanamo does more harm than good, though some in Congress take a not-in-my-backyard approach to relocating the detainees. 

Adm. Mike Mullen, chairman of the Joint Chiefs of Staff, told ABC's "This Week" that he agrees the prison is harming security. 

"The concern I've had about Guantanamo in these wars is it has been a symbol, and one which has been a recruiting symbol for those extremists and jihadists who would fight us," he said. "That's the heart of the concern for Guantanamo's continued existence, in which I spoke to a few years ago, the need to close it."

Mullen said Guantanamo needs to close, and "we're all working very hard to meet" Obama's January deadline. 

Sen. Ben Nelson, a moderate Democrat from Nebraska, did not question the value in closing the Guantanamo detention camp. 

Rather, he said Democrats are withholding funding because they need to see a plan that keeps dangerous terrorists off U.S. soil. 

"Whether it's closed or not, we have to have a plan in place that outlines how we deal with the people who are incarcerated there," he told "FOX News Sunday."

Illinois Sen. Dick Durbin, the Senate Democratic whip, told NBC's "Meet the Press" he has no objections to keeping Guantanamo detainees at super-maximum security facilities on U.S. soil.