The Americans have taken this stance for purely selfish reasons. They like having a poodle to do their bidding in the EU which is still, despite the best efforts of the economic incompetents in charge, one of the main competitors to the US. The UK outside of the EU would be a significant challenger to the US, particularly with the Commonwealth Free Trade Area that UKIP proposes. The EU without the UK bailing it out would be much poorer and unable to buy as much American tat and don't forget that this is a socialist president supporting the socialist EU empire.
You have to admire the Americans for standing up for their national interest but leaving the EU is in ours and Obama can bog off.