First, whatever money they think they will save on salaries will have to be counted against what it will cost to terminate. People will still have leave balances that are typically paid out upon termination. Workers with long work histories may have quite a bit of leave to be paid out. If these ghouls have any sympathy then severences will be needed. Both of these would count against any potential savings.
Second, if you fire someone then you owe unemployment compensation to anyone who qualifies. That will be a drag on the economy. Unemployment increases are a double whammy. You loose tax revenue and you have to pay out unemployment compensation.
Third, you have to hope the pin heads who are going to do the firing do it right. If not, there are going to be a lot of legal expenses that will have to be paid out.
Fourth, I hope someone tracks just where these positions are being eliminated. If more blue states than red take a hit then you know this is all politically motivated.
Fifth, someone better track if work done from these eliminated positions isn't just transferred to more expensive (and politically connected) private sector jobs.