Normally in a recession and recovery government at all levels increase public employment - this has happened in every GOP administration - and much of that increase is funded by federal government grants to the state and local governments. But since the Stimulus, the GOP has blocked any substantial help for the states, and in GOP led states severe austerity cuts have been the rule - even including GOP governors rejecting projects fully funded by the federal government. The economic cost of this is far more than just those 600 thousand jobs - the spillover effect on private business and local economies has been devastating - when you factor in all these effects the total job cost of austerity has been estimated at 2.3 million jobs.
The result of GOP obstruction with those two things cost us 2.3 million jobs and 1.9 million jobs respectively. US employment as of May 2011 is about 155 million jobs, which means those 4.2 million jobs that the GOP has prevented account for 2.7% of the unemployment rate. But let’s be fair, there is a small amount of overlap in those jobs - a small portion (about 8%) of the American Jobs Act would have gone to State and Local governments to pay for teachers, first responders and the like - although for the most part it would have just prevented further layoffs rather than resulted in new hires. It is also very likely that without the economic wrecking of GOP obstructionism the labor participation rate would be higher - so instead of a reduction of unemployment to 5.5% it would be slightly higher, but still well under 6%.