We could only hope that a few civil service employees would take the hit, but I won’t hold my breath.
Honestly, aside from a few totally unnecessary agencies (Dept. of Education anyone?) most of the cuts could come from letting people retire who will be retiring, and just not replacing them, or shifting around responsibilities.
Getting rid of the unions would probably fix most of the rest of the problem, and make government employment more or less on-par with the private sector.