The new year has begun with no end in sight to the partial government shutdown, and a lawsuit has now been filed on behalf of federal employees who are working without getting paid.

The American Federation of Government Employees is suing the government for forcing "essential" employees to work paycheck-free during the shutdown.

The shutdown affects nearly 800,000 federal workers, or about 25 percent of the government.

Despite the financial strain for workers through the holidays, President Donald Trump has stood firm on his demand for funding for a wall along the border with Mexico.

"It's not going to be open until we have a wall, a fence, whatever they'd like to call it," Trump says.

Trump claims "many" federal workers have communicated that the shutdown should continue until funding is secured for the wall. But if the lawsuit is any indication, that's not the case, and what workers really want is to be paid.

More than 400,000 government employees are working without pay. The others have been furloughed.