Federal Employees Civil Relief Act This bill establishes a framework to temporarily suspend certain judicial and administrative proceedings against a federal employee or contractor during a shutdown. Under the bill, a shutdown is a period in which (1) there is more than a 24-hour lapse in appropriations for any federal agency or department because a regular appropriations bill or a continuing resolution has not been enacted, or (2) the debt of the federal government is greater than the statutory limit. A federal worker (i.e., an employee of a government agency or contractor) who is furloughed or required to work without pay during a shutdown may apply to a court for a temporary stay, postponement, or suspension with respect to any payment of rent, mortgage, tax, fine, penalty, insurance premium, student loan repayment, or other civil obligation or liability that the worker owes or would owe during the duration of the shutdown. The bill includes related provisions that restrict evictions, foreclosures, the enforcement of liens, and the termination of insurance policies during a shutdown. It also provides for the deferral of federal income taxes and student loan payments during a shutdown. The Department of Justice may commence a civil action against any person who engages in (1) a pattern or practice of violating the requirements of this bill, or (2) a violation that raises an issue of significant public importance. A person aggrieved by a violation of this bill's requirements may also bring a private right of action.