Biden made the remark moments after introducing Obama at the signing of the controversial bill on Tuesday and may not have realised that his voice was being picked up by the podium microphone.
In response Robert Gibbs, the Whitehouse Press Secretary later Tweeted: "And yes Mr Vice President, you're right."
Senior Obama adviser Valerie Jarrett said that Biden's loose talk was "part of what makes the vice president so endearing...We wouldn't change him one bit."
Former Senate colleague Lindsey Graham said, "If there were no gaffes, there'd be no Joe. He's someone you can't help but like."
This is not the first time Biden has been caught using the F-word. He used it when speaking to another senator last year, also into an open microphone.
WARNING: CONTAINS STRONG LANGUAGE