People are very interested in partisan politics. Political partisans are very interested in the presidency. The president is an important player in federal budget debates. And thus people are very interested in questions about federal government spending "under Obama." But the national economy doesn't care about why money gets spent or which level of government spends it.
And taken as a whole, consolidated government spending—federal, state, and local—simply hasn't surged. You can take the beginning of the recession or the beginning of the Obama administration or whatever you like as your starting point and it still hasn't happened. Spending continued on essentially the previous trend throughout the official NBER business cycle dates, and then flattened out in a nearly unprecedented way once the economy began.
If you believe that restraining government spending should supercharge private sector economic activity, then you ought to know that since 2010 we've been living through a nearly unprecedented level of public sector spending restraint. Counterfactuals are, of course, hard. Perhaps private sector growth would have been even weaker had public sector spending risen at a more normal level. But an unusually low level of spending growth isn't a policy we might try in the future, it's a policy that we're trying right now and have been trying for the past few years.