I'm a bit late to the party on this one, but during the recent showdown over shutting down the government I was a trifle worried, being a government employee and all that. Apparently we're out of the woods until the end of my service, but I was still a bit curious about how it works.
First, if a shutdown looks likely, each agency has to submit a budget request to the Office of Management and Budget. The administration then gets a bit of leeway as to what gets funded and for how long. In our case it seems we were set both for staff and volunteer payments so long as the shutdown didn't go too long. (See here for more.) However, the Peace Corps appropriation has been reduced by $25 million, so there has been some scrambling; here the newest group of volunteers was cut by quite a bit in response.
What a pain in the ass.
UPDATE: I forgot to mention that Aaron over in Azerbaijan had a related post awhile back.