This power is pretty overrated.
How often have you turned on the TV and seen a network cover the entirety of one of Obama's speeches/press conferences, other than a major speech like the state of the union? Usually they cut away to something else after a little while or don't cover it at all, except maybe on a morning show.
Non-TV media generally cares even less.
Get on TV every single night, spread awareness about what's happening there, tell US citizens that we need to lead by example, and use the propaganda machine to create positive change, for once.
More importantly there's a limited amount of political capital you have as POTUS. While you may think Obama should have directed more of this to closing Gitmo, I think the big ticket accomplishments he spent that political capital on such as ACA were more important.
And it's not clear at all that Obama could have successfully closed Gitmo even had it been a higher priority of his. It is clear that he immediately ended interrogative torture [2] and made efforts to close it. There's still force feeding but that's also an issue in us prisons so closing gitmo and sending the detainees to other prisons is not necessarily solving anything there.
[1] one early study here: http://www.latimes.com/business/hiltzik/la-fi-mh-obamacare-w...
And Gitmo was just an example, not necessarily saying it would even be at the top of my list. Of course sending the detainees to other prisons is not the answer. These people need to be freed, now. Same deal with the multitude of other US military prisons and CIA black sites.