The President signed a bill last Friday that prohibits any funding for the transfer of gitmo detainees in the United States. The bill also has a provision requiring a stringent certification process in order to provide funding for transfers to other countries. Check out
this link for the complete details about the law and the provisions.
In the end, Guantanamo Bay will likely remain open beyond the next election. Though, to be fair, President Obama did issue a signing statement with the above bill stating his objections to these provisions, which means his administration may not enforce them. Also, Obama tried to get $60 million from Congress in 2009 to close the detention center, but Congress blocked it. Therefore, these protesters need to be in front of the Capital Building, not the White House.
However, President Obama has the authority as Commander-in-Chief to close this facility tomorrow if he wants, but then the question becomes what to do with these detainees. One option is to put them in already established military bases or prisons, but spreading these detainees out from the already centralized location could only cause more logistical problems. There isn't an easy solution, but this dilemma does highlight something in particular - the facility should never have been built - thanks George Bush.
Edit: Also, if your wondering about the possibility of building a new detention center in the US for the Gitmo detainees, go ahead and scratch this out because another provision of the aforementioned bill specifically prohibited funding for this and President Obama did not object to his provision in his signing statement.