I think the President SHOULD have said "The Federal employment sector is doing just fine". Here is the proof in one easy graph...

Planet Money at NPR has been following the change in government jobs at the Federal, State and Local level since the beginning of the recession. 

Due to the first large stimulus package in 2008 that aided states in budget crisis, employment actually increased for State and local governments during the downturn.

As you can see from the graph below since the exhaustion of Federal stimulus local government employment has taken the biggest hit, losing over 400,000 jobs, followed by State level jobs at loss of about 100,000.

Federal employment has remained elevated ABOVE pre-recession levels.

You could say "Federal employment is doing fine". State and local not so much.

How does this compare to private sector jobs?

Looking this next graph you can see the magnitude of government job loss, in relative terms, pales in comparison to private sector job loss.  We still have a long way to go....