No, Jamie, presidents don't shoulder the blame for high inflation, recessions, or low/no inflation and economic recoveries. But the media and other voices would have us believe they do. So, if Bush I and II were blamed for the economic problems on their watch, then Obama deserves blame on his.
Also, while he does not legislate, a president does push legislation, and Obama has pushed for many measures that have adversely affected the economy. The spending and the prospect of higher taxes are two major factors affecting our economy, and both lie in Obama's lap.