Bill Clinton's administration used a systematic approach that trimmed some 400k jobs from the government and also balanced the federal budget. It was even done in a bipartisan fashion. I don't know why a similar approach could not be used now with great success, especially considering Republicans control both legislative bodies and the executive office. What is happening now is just chaos.
To roses04's point about private sector layoffs, people in the private sector are paid more than employees who do the same job in government and are often given separation packages that help soften the blow of being laid off (buffering the risk of being laid off). Folks who work for the government often accept the lower wages because they want to serve their country and are willing to accept lower wages for the (supposed) stability these positions offer. Just jettisoning people with no rhyme or reason and no warning is just cruel. And these probationary employees (who are being fired in large swaths) would be the ones making the lowest wages; generally speaking downsizing is more successful when you move on from more tenured, higher paid staff.
I'm all for downsizing the government, but I disagree with a strategy that is unorganized, and likely unlawful at many junctures. Firing and rehiring is inefficient and wastes taxpayer dollars. Having to defend numerous lawsuits wastes taxpayer dollars. Breaking a bunch of laws hoping you will redefine a few legal precedents in the courts to me is unethical. Again, Republicans control all chambers and could pass new legislation if they want to change the course of business (such as Humphrey's Executor et al).