The top Republican in the House and a senior White House adviser on Sunday debated a plan for closing the U.S. military prison at Guantanamo Bay and moving some of the terrorism suspects held there onto American soil.

"They want $500 million from this Congress to rehabilitate this prison in northwest Illinois," John Boehner, R-Ohio, said on CNN's "State of the Union." "I want to see who the members are who are going to vote for this. I wouldn't vote for this if you put a gun to my head."

Two months past President Obama's self-imposed deadline for closing Guantanamo, the facility remains open as details of where to house the suspects are being worked out.

The Obama administration wants to buy and prepare the idle prison in Thomson, Illinois, to house many of the remaining Guantanamo detainees, who number about 190. Several lawmakers in the House and Senate have vowed to block the funds.

"Obviously, there are a series of issues related to this, some of them legislative, that have to be dealt with," senior White House adviser David Axelrod said. "We have made good progress. You know, when we got there, the legal status of many of the people there was unclear. We had to go through a process of really sorting all of these cases out. We are beginning to work those cases."

Asked how much longer it would take, Axelrod said he doesn't know. "It's going to take a little time, but I am absolutely convinced we are going to get that done."

Video: Boehner backs Guantanamo I wouldn't vote for this if you put a gun to my head.

--Rep. John Boehner, R-Ohio

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Boehner, however, said that Guantanamo is a "world-class facility" and is the proper venue for conducting military trails for the suspects. A proposal to try some of the suspects -- most notably Khalid Sheikh Mohammed, alleged mastermind behind the September 11, 2001, terrorist attacks -- in the United States has drawn fire from critics, including many Republicans. Officials in New York City, including Mayor Michael Bloomberg, are opposed to conducting Mohammed's trial in Manhattan, because of the high cost and potential disruptions.

"The original decision was to try him in New York," Axelrod said. "Local authorities were receptive there at the beginning, they changed their view on that. That has to influence our thinking. The question becomes ... what possible venues would there be? And is it worth reviewing the entire decision?" He said there are "a range of options" for trying Mohammed.

"I think [Guantanamo is] the appropriate place to hold these prisoners," Boehner said Sunday. "And they can do the tribunals right there at Guantanamo. There's no reason to bring these terrorists into the United States. No reason to increase the threat level here -- because they're here, their friends may want to come.

"It makes no sense to me," Boehner said. "And I don't think the Congress will appropriate one dime to move those prisoners from Guantanamo to the United States."

Earlier this month, a senior administration official told CNN that White House advisers are considering recommending Mohammed be tried in a military court instead of a civilian one in New York City.

Attorney General Eric Holder announced his intention to try Mohammed in a New York civilian court in November.