Three Republicans join most Senate Democrats in a vote to loosen restrictions on transferring detainees out of the prison at Guantánamo Bay, potentially leading to its closure

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In a surprising win on Tuesday night, the White House and top Senate Democrats successfully defended provisions in the National Defense Authorization Act (NDAA) that would loosen restrictions on transferring detainees out of Guantánamo Bay, advancing President Obama’s goal of closing the facility by a margin of 55-43. A vote in favor of final passage on the entire NDAA is expected in early December, after which it faces a likely fight in conference with the House’s version of the bill, which maintains the transfer restrictions.

One Democratic Senate staffer who supports closing the Guantánamo Bay prison called the result, “The strongest vote that I can recall on this issue.”

As recently as early November, Democratic Senate aides participating in the fight to loosen the transfer rules described the politics of the vote as “difficult” but “not impossible” and said those whipping the vote were five or six votes short of the bare majority they needed to defend the provisions. The challenge was to win over swing-state Democrats who had opposed moves to close Gitmo in the past, and to hold supporters facing re-election in 2014.

(MORE: Seeing New Opportunity, Obama Lobbies on Key Gitmo Vote)

In Tuesday’s vote, the White House did both. It held Mark Begich of Alaska and Mark Udall of Colorado, two Democratic supporters facing re-election, and won over three former Democratic opponents who are not up in 2014. That allowed Democrats Kay Hagan of North Carolina and Mark Pryor of Arkansas, both of whom are in tough fights next fall, to oppose the bill.

Perhaps most surprising, and most heartening for those seeking to close Gitmo, the White House picked up three Republican votes: John McCain and Jeff Flake of Arizona, and Rand Paul of Kentucky. Paul’s vote suggests potential support among libertarians for the loosened transfer restrictions in the GOP-led House, but the measures still face an uphill battle before they become law. The GOP has strongly opposed measures that could lead to the closure of the prison at Guantánamo Bay, and for many that opposition remains.

Several factors have contributed to the sharp change in the political atmosphere over the issue, however. The rise of libertarian opposition to executive-branch authority, especially “law of war” powers exercised by the President, is one factor. The cost of the Gitmo facility, relative to detaining terrorists in the U.S. or abroad, is another. It costs anywhere from $900,000 to $2.7 million per inmate per year to detain a terrorist in Guantánamo Bay, whereas it costs around $60,000 a year to detain one at a supermax facility. Several al-Qaeda terrorists are currently detained at such facilities in the U.S.

The ultimate test of the politics will come in December during the House-Senate conference. The NDAA is typically one of the last bills passed before the end of the year.