US federal employees go through a one-year probation during which they can get fired for any number of reasons. After that it is pretty hard. I don't think part-time employees are part of that civil service process, though, but being the government there are probably rules written down somewhere. Check with your personnel office whether you can be let go "at will" (I think that's the expression) or "for cause". If it is only "for cause" you can ask what those causes are.
I don't know if the government works this way, but some private employers who don't feel they can fire an employee just cut their hours until the employee can't survive.
- Kate