Without austerity cuts at the State level, unemployment would be significantly better.
So, yes, funneling more money to states to keep their teachers and other workers employed would have been a sound way to deal with the recession.
Where conservatives should focus their attention is during boom years when everyone and their mother in government wants to spend more in response to the higher tax receipts. Conservatives should insist on holding the line on spending and reducing the debt then. Instead, they generally call for lower tax rates to pair with the Democrats calls for more spending.