Economics:
The debate about whether or not the stimulus worked or failed will likely go on for quite some time. The Council of Economic Advisors (all of whom were appointed by Obama), however, show that the argument for the stimulus is getting harder to make. According to the report, close to 2.4 million jobs were either gained or saved. The stimulus cost more than 650 billion dollars to date. This means for every job gained or saved the total cost to the taxpayer is more than 250,000 dollars. That is a pretty high cost on a per job basis. The full report can be found here.
Additionally, when we look at what Obama's economic team said the stimulus and bailouts would do compared to what actually occurred, the picture becomes even clearer. Christian Romer, then-Obama's Chief Economist, said that the stimulus would keep unemployment down below 8%. This, of course, proved to be false. As Ms. Romer expected the unemployment to decline it was increasing. She later said she regretted that comment as can be found in this article.
The argument that the stimulus has worked is getting harder to make. There are still respected economists (Krugman, Stiglitz, etc.) who are fighting for the stimulus and even calling for another one. The say the economy would have collapsed if the bailouts hadn't occurred. There is simply no way we will ever know that.
Overall, there does appear to be plenty of evidence to support Mitt Romney's claim that Obama made the recession deeper and harder than it had to be. Certainly the 2.4 million jobs gained or saved (if an accurate number) is good. The problem is that 250,000 dollars per job is a little tough to swallow, especially considering we had to borrow all of that money and our children will be forced to repay it with interest. The heavy stimulus cost also added to currency concerns and added even more instability to an already unstable marketplace. Those effects likely overpowered the governmental spending, which is why we have seen the unemployment rate increase since the stimulus, as well renewed inflation fears and other currency concerns.
Politics:
This is a winning argument for Mitt. He will be asked a series of similar questions that are all slightly different so he has to explain a great deal of information which will allow negative ads calling him a flip-flopper. Honestly, that's a small price to pay. These kinds of attacks focus the conversation on the economy where Romney is, by far, the strongest candidate. Additionally, it puts obama in the uncomfortable position of having to argue the stimulus worked even as more and more people get pink slips.
If this election (both primary and general) focus on the economy, Romney is in excellent shape. This is the correct line of attack against Obama. Additionally, the negative DNC ads show they are obviously worried about running against Romney. They know that if he wins the nomination, the election will have to be about jobs and the Obama administration's terrible records on them.