Democrats lost the fight for public opinion over the stimulus -- indeed, they lost so badly that the entire debate now focuses on how much anti-stimulus we should impose. Yet I don't think they should give up on using this issue against Republicans. You have, basically, the entire economic forecasting field predicting that the Republican budget would cost hundreds of thousands of jobs. That's a powerful political weapon.
Republicans are pushing back on the economic forecasters by noting that those forecasters also supported the stimulus, which is true. If the public opposed stimulus, the reasoning goes, they should support anti-stimulus.
But I think the actual thought process of the majority of the public is a lot messier. People don't trust politicians, especially when economic conditions are worsening. People won't believe that a politicians' economic stimulus is saving jobs. At the same time, that same cynicism could lead them to believe that another politicians' plan is costing jobs. Conservatives want to believe they won the public opinion war because the public is deeply committed to Austrian economics, but the truth is that, in a bad economy, people will tend to believe the negative claim over the positive one. Now that Republicans are the ones trying to change the status quo, that factor is a powerful weapon for Democrats.