GLAESER: Why government spending cuts won’t kill too many jobs. “[T]he U.S. is far enough along in its recovery that it can begin balancing its books. An impressive new series of papers has estimated the impact of public spending on jobs during the recession, and concluded that we can make moderate budget cuts without sending the economy into a tailspin…If we cut only $50 billion, this should mean 400,000 fewer jobs, and possibly less if the effect of public spending on employment is weaker today than it was during the recession. That's a serious loss, but if private-sector job creation continues at its current annual rate of 1.9 million a year, private-sector growth could offset that loss in less than three months.” Edward Glaeser in Bloomberg.

Doesn't the multiplier estimate job loss across the economy, including the private sector?  So if there are 400,000 fewer jobs, some of those will be lost in the private sector (federal contractors, for instance, or companies that had benefitted from cut government programs) and therefore the private sector won't be creating jobs at its current annual rate of 1.9 million