Employment Law Questions? Ask an Employment Lawyer.
Yes, they can. It's not as easy as suing a private employer, because the government has immunity and have only released that immunity in very specific ways.
But yes, you can file a suit against the federal government for violation of your due process rights in employment, discrimination (based on race, religion, gender, age, disability or FMLA use) or retaliation.
You must first complete the internal grievance process, because you have finish all administrative remedies before you can successfully file suit. You can do that through an internal EO complaint. Once that is done, if you are not satisfied with the outcome, you can then file a complaint through the federal torts claims act for the offenses.