That's a reasonable way to view this. Good to see someone taking a balanced approach.
It is definitely true that Obama would have spent more if he had gotten his way. It is also true that, given the economic situation he was dealing with, he's been far more responsible than Bush Jr. was with what he inherited.
It's also worth pointing out that many economists believe that spending *should* have been higher to help break us out of recession. And that much of the reason for the high deficits is decreased revenues due to tax cuts and loss of income because of the recession itself.
Bush sank himself when he pulled the incredible mistake of Iraq. It seems that everyone likes to spend, it's a matter of on what. If he hadn't been that stupid then the numbers would have been different, but "could" and "did" are different things.
Also the solution of spending one's way out of a recession is rather simplistic since the results are dependent on the nature of the economy at the time. I believe that spending doesn't address the core problems of unemployment and stagnant wages, which I attribute to outsourcing and the drive to downsize further. That's driven by costs and the disconnect between what is beneficial to the boardroom and to the nation. Throwing money into the economy will most likely mean that it will be spent overseas, increasing automation at a time when replacing people with machines is not helpful, and even if it did help it would be temporary while the problem as I see it now is virtually institutionalized.
Better than spending (although well thought out targeted spending I do not disagree with) would be to change the business climate with intelligent regulation to make boards more accountable in fact rather than theory to a larger number of shareholders, not just the members of the "old boy club" who are fund investors which are part of the unaccountable class who determine company policy and their own compensation packages at the expense of the employed (or under or unemployed). To encourage a climate where money is spent domestically an environment of accountability needs to be fostered. Note I said intelligent. The simplistic idea of taxing the top bracket does nothing to provide to motivation for long term well paying domestic jobs, indeed it feels good, but is in fact harmful. If taxed to they have less money, they'll squeeze more out of their remaining workers to compensate. I don't see that as very useful.
The ultimate solution is to work to have government facilitate an economy where the private sector finds it in their best interest to provide good jobs, which solves a great many problems, not least of which are recessions.