Suing a .gov entity can be profitable. If you have anything resembling a cause of action, by all means file suit. They'll likely roll over and settle. That's windfall.
Actually, except for a few specific permissions, you can't "sue" the federal government. You can file a federal tort claim, which is what you file when, for instance, a government car hits yours and damages it.
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FEDERAL TORT CLAIMS ACT
Citizen's Remedy Against Torts Perpetrated by Government Personnel
Title 28 U.S.C. § 2675(a) provides, in pertinent part:
"An action shall not be instituted upon a claim against the United States for money damages for injury or loss of property or personal injury or death caused by the negligent or wrongful act or omission of any employee of the Government while acting within the scope of his office or employment, unless the claimant shall have first presented the claim to the appropriate Federal agency and his claim shall have been finally denied by the agency in writing and sent by certified or registered mail. The failure of an agency to make final disposition of a claim within six months after it is filed shall, at the option of the claimant any time thereafter, be deemed a final denial of the claim for purposes of this section."
Title 28 USC § 2401(b)
A tort claim against the United States shall be forever barred unless it is presented in writing to the appropriate Federal agency within two years after such claim accrues or unless action is begun within six months after the date of mailing, by certified or registered mail, of notice of final denial of the claim by the agency to which it was presented.
Title 28 USC § 2675:
The failure of an agency to make final disposition of a claim within six months after it is filed shall, at the option of the claimant any time thereafter, be deemed a final denial of the claim for purposes of this section.
Title 28 U.S.C. 2401(b) requires the claimant both to file the claim with the agency within two years after accrual of the claim and then to file a complaint in the District Court within six months after the agency denies the claim.
Title 28 USC § 2401(b)
A tort claim against the United States shall be forever barred unless it is presented in writing to the appropriate Federal agency within two years after such claim accrues or unless action is begun within six months after the date of mailing, by certified or registered mail, of notice of final denial of the claim by the agency to which it was presented.
Title 28 U.S.C. § 2675(a) provides, in pertinent part:
An action shall not be instituted upon a claim against the United States for money damages for injury or loss of property or personal injury or death caused by the negligent or wrongful act or omission of any employee of the Government while acting within the scope of his office or employment, unless the claimant shall have first presented the claim to the appropriate Federal agency and his claim shall have been finally denied by the agency in writing and sent by certified or registered mail. The failure of an agency to make final disposition of a claim within six months after it is filed shall, at the option of the claimant any time thereafter, be deemed a final denial of the claim for purposes of this section.