Some of those employees will no doubt collect unemployment insurance, so the government's obligation to them won't disappear with their jobs.
Boehner didn't cite a source for the claim that Obama had added 200,000 employees to the federal payroll. And he said he didn't have an estimate of how many jobs would be lost as a result of the GOP cuts. But once the extent of the cuts is finalized, economists will provide them. And then we'll have an answer for a question Boehner made famous during the 2010 campaign: "Where are the jobs?!"
Update: Ed O'Keefe of the Washington Post reported last September that there were only 20,000 more federal employees under Obama in 2010 than under George W. Bush in 2002 -- and that, on a per capita basis (federal employees per 1,000 Americans), it's at the lowest level at least since 1962.