Honestly, if Obama decided he could not or would not close the prison, I don't foresee the next president, regardless of party, doing so either. Not trying to find excuses for Obama not doing that, but from looking at presidents throughout history, they all seem to have a finite limit on how many battles they can choose to fight (and maybe get passed by a wishy-washy congress).
Issues like the National Healthcare Act just barely managed to get passed in Obama's first term when his party had control of congress still. Based on that and how long it took to get pushed through, something just as touchy as Gitmo would be just as tough and probably impossible with the extremely partisan state of congress right now.
The impotency of the US Government right now to accomplish even trivial things is also a mixed blessing. When one party controls everything, we get situations like the first decade of the 21st century where the majority party gets to basically rubber stamp every whim and desire. With two party deadlock, issues are not being solved, but the alternative of either party being in full control is not always desirable and becomes a "be careful what you wish for" scenario much of the time.
Though neither party is really that different from the other on most issues, when one has control of the presidency and the other does not, the opposing party will go out of their way to distinguish themselves for the sake of being contrary. A few months ago there was a discussion on NPR about the partisanship shown in congress being related to the gerrymandering done in redistricting last time. The lines being drawn up to make each district more polarized to one side or the other makes any representative that faces election every 2 years less likely to compromise (versus their counterparts in the senate every 6 years), for fear their constituents will end up nominating someone even more polarized than they are perceived to be.
I don't know if that is entirely true as gerrymandering is not new (or new to criticism), but it does explain some of the congressional silliness in the past 5-6 years as the house of representatives has been opposed to compromise more often than the senate. It would take more statistical research to decide if gerrymandering is causing congress to become gradually more polarized over time or if it varies with each time the congressional lines are being drawn up. Looking at the number of bipartisan bills proposed and passed over the last 100 years as well would be a starting point.