Not necessarily more, but it would require a different distribution. Money would need to be spent to relocate the prisoners. Congress has blocked that reappropriation.
Quoting Wikipedia:
On May 20, 2009, the United States Senate passed an amendment to the Supplemental Appropriations Act of 2009 (H.R. 2346) by a 90-6 vote to block funds needed for the transfer or release of prisoners held at the Guantanamo Bay detention camp.[14] President Obama issued a Presidential memorandum dated December 15, 2009, ordering Thomson Correctional Center, Thomson, Illinois to be prepared to accept transferred Guantanamo prisoners.
On January 7, 2011, President Obama signed the 2011 Defense Authorization Bill, which, in part, placed restrictions on the transfer of Guantanamo prisoners to the mainland or to foreign countries, thus impeding the closure of the facility.[17] U.S. Secretary of Defense Gates said during testimony before the US Senate Armed Services Committee on February 17, 2011: "The prospects for closing Guantanamo as best I can tell are very, very low given very broad opposition to doing that here in the Congress."[18] Congress particularly opposed moving prisoners to facilities in the United States for detention or trial.
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In short, congress passes bills to prevent Obama from closing Gitmo. Obama signed one or more of those in order to balance other political agendas. The annual Defense Authorization Act is a particularly politicized bill that congress is known to use as an offensive weapon.
Does congress control how Gitmo is run? My understanding is that the President is in charge of the how (execution of the law), and congress only controls the what.
This is true in theory, but in practice, Congress can be as specific as it likes about how the money is allowed to be spent.
For example (from the NDAA 2013, Section 1022)[1]:
"(a) In General- No amounts authorized to be appropriated or otherwise made available to the Department of Defense for fiscal year 2013 may be used to construct or modify any facility in the United States, its territories, or possessions to house any individual detained at Guantanamo for the purposes of detention or imprisonment in the custody or under the control of the Department of Defense unless authorized by Congress.
(b) Exception- The prohibition in subsection (a) shall not apply to any modification of facilities at United States Naval Station, Guantanamo Bay, Cuba."
