The following is not meant to defend Obama. He is a horrible president...
The Fed's ZIRP policies are not dictated by the US government. Instead, many of the government's actions are caused by the FED.
Also, don't forget that it was President Bush and the Republicans who partnered with the Demon-rats and got the first TARP bill passed.
What if you were president of the US and knew that you had two choices:
1) Keep debt levels somewhat low and see the nation go through a Greater Depression on your watch, or
2) Start creating new debt as fast as possible through all means at your disposal (after all, the US government is somewhat limited in its ability to create new debt, since it has to fund all loans that it originates). This would create the illusion that things are getting better, while making the entire citizenry even more debt slaves to the largest international banks.
Almost all politicians, Republic and Demon-rat alike will choose option 2. Bush did. Obama did. Remember "Cash for Clunkers"? Do you see all of the federally-subsidized road construction projects going on all over the US right now? How about all of the student loans that are being distributed like candy?
If I was president I would immediately seek to abolish the Fed, and have the currency of the US handled by the US Treasury - and not be debt-based. Currency would only be paid out and circulated based on the completion of underlying labor.
Of course, the international banks could respond to that by immediately shutting down their financial clearing houses and refusing to process any transactions. This would collapse the world economy overnight.
So...how much economic power does the president really have? The answer is: not much. The bankers control the game, and can take their ball and go home if we all refuse to play by their rules. That's a pretty bad place to be. We stopped being the "Land of the free" a long, long time ago - when we adopted debt-based currency.