Remember "It's the economy stupid?" The first President Bush certainly does, because that phrase famously summed up the soon-to-be President Clinton's campaign focus in beating him. Here's the thing – Clinton ended up getting too much credit for the economic recovery that occurred during his first term, and Bush-the-first didn't get enough credit for making the tough and politically disastrous policy decisions that kick started the recovery in the first place.
Why bring that up now? Because it's interesting to see how President Obama is blamed for things that he literally has no control over, like high gas prices, but gets no credit for things he had a direct hand in, like an improving economy. He is also being criticized for budget deficits that were largely made necessary by the policy decisions of his predecessor, President Bush-the-second. Could Obama have made policy choices that kept the deficit from growing as much as it did in his first term? Sure, but many economists think that would have been much worse for the economic recovery we're seeing. In fact some argue that his policies weren't aggressive enough – that larger short-term deficits might have led to a faster, steeper economic recovery.
What further complicates the issue in this election cycle is that President Obama came into office as the US economy was in an unprecedented-in-our-lifetime freefall. In the same way that it's difficult to prove a negative, it's also difficult for a sitting President prove that the economy could have been in worse shape if his policies had been different. Quite frankly it's easier for a challenger to say that things could/should have been much better and that it's the President's fault that they aren't; he literally doesn't have to prove it since it's a matter of opinion. That's how Clinton took out Bush Sr. and that's how Romney is trying to take out Obama.
It remains to be seen if the recent economic improvement will be enough to convince voters that Obama is worth keeping around. If it's not, Romney will inheret a growing economy and unless he really screws up he'll be given far more credit for it than he deserves.