Obama ran for office on a pledge to close Guantanamo, and he could have done so by executive order. He didn't, and that should tell you all you need to know about the nature of the American presidency.
There was a HUGE faction in congress (they go by a name that rhymes with schmepublicans) that would have punished him severely if he had done that. The presidency is not as all-powerful as some people think it is, sometimes this is good, sometimes not so much.
When President Obama took office, Democrats controlled both the House and Senate. You can't hang this one on Republicans. Both parties were equal participants in keeping the Guantanamo detention facility open.
Congress sets the annual federal budget. The Democrat controlled Congress literally allocated dollars to run that facility. If Democrats actually wanted to close it they could have eliminated funding, but they specifically chose to keep it multiple times.
Early in a new President's first term, "I promised over and over to do X while I was running for President, and the American People very clearly voted for that" is d*mn good political cover for doing X.
There was an opportunity for Obama to have a much more effective and bipartisan presidency early on. It wouldn't have been a friendly relationship, but certainly a more effective government. He rammed Obamacare through Congress very early in his presidency and that pretty much removed his ability to do anything else in his first term.
There was good faith negotiation about the plan. It was very close to what the Republican plan was. The problem was that Mitch McConnell stated publicly that he was going to block everything that Obama did. The Republicans blocked stimulus funding. To claim that the failure of bipartisanship was Obama's is to ignore the facts as stated by the Republicans at the time.
Also, and I'm really not trying to be snarky, that statement sounds like something the child of abusive parents would say. If only Obama had been quiet, they would've left him alone. That's a no-win situation, I think.
I'm answering your question by suggesting that Obama could have gotten much more done if he had not been so extremely partisan from day 1. When it became clear he was not going to negotiate any changes to the monumental Obamacare law and pass it through on a partisan vote, the only natural response for Republicans seeking to effect their own policy agenda was to block as much as possible. In effect Obama, rather than choosing a 90/10 or 80/20 ratio of democrat to republican polciies to be passed, said there was no point in allowing any republican policies through. And so the only natural response was for Republicans, as the minority, to respond in kind until the next election.
A more mathematical explanation would be that if every law was 80% Democrat policy and you were able to pass 100 policies a term, you could get 80 of your policies through in a single term. You might think getting 100% of every policy in a bill would be better but that might mean you only get to pass 50 policies a term because of increased partisan tensions. Even at 100% that's only 50 Democrat policies instead of 80.
I'm sorry, but you're ignoring the actual things that happened. There were good faith negotiations with the Republicans about Obamacare and post-crash stimulus and the Republicans chose to unanimously vote against them because they saw a partisan advantage to doing so.
I'm not ignoring anything. Obama was successful in his first year, in part because of how much effort he put into being bipartisan. He did not have much success in getting Republicans to vote for his massive landmark policies, but his Supreme Court nominee sailed through confirmation.
Generally, Republicans were very engaged in solving problems in the first year, but faced the reality of a democrat supermajority. Obama made many concessions in the bills he passed despite not getting many Republicans to vote.
There's nothing inconsistent there with a contentious but effective government. Sure it would be nice to have gotten more Republicans to vote yes, but the process was working.
After he passed Obamacare, in which he abandoned all negotiations with Republicans and flexed his supermajority power, the only appropriate response was stonewalling.
Punished him how? Were the schmepublicans not already turning up the drama dial to 11? What further recourse did they have to make things worse for him?