Most people don't accuse him of blaming Bush, just his supporters. I haven't noticed much of it on this forum but literally every time I get into a political argument with an Obama supporter in real life they will either end up just refusing to continue the argument (which I'm generally fine with, since they're typically the ones who initiate it) or end up saying something to the extent of "yeah, well at least he didn't waste money on two wars!!" or "yeah well at least he didn't crash the economy like Bush!!" as if the actions of Dubya were an appropriate standard by which to judge Presidents.
But it's not like McCain or Romney would have done any better either.
There are valid criticisms to be made of him (NSA, net neutrality, financial reform, etc.), but the ones concerning the wars in the Middle East and the economy really don't hold any water at all. Especially those two, because those wars were doomed from the get-go and the Republicans have been egregiously uncooperative on fiscal policy.