Odds of Hanging On
Staying where you are depends a whole lot on where you are, that is, in which part of which sector you work (source). If you're one of the many thousands of civil servants working in government, your job is safe as long as the people believe you (or the public administrator who put you there) should have it.
Non-profit workers can stay as long as the funds are there for the position, while private consultants will rely entirely on their business cred. Of course, no job is really safe when it's a line item on a budget somewhere. If anyone is more in charge than you, remember to keep them happy.
On the bright side, there are so many different places to use your public administration degree that if one door should close, there are at least a dozen others you can try knocking on.