A bill signed into law by President Obama late Monday will keep paychecks flowing to members of the military and many Defense Department civilians despite the government shutdown.

The Pay Our MilitaryAct, which passed the House and the Senate without opposition, represented a rare moment of unanimity in Washington, but few were claiming that it marked true bipartisanship.

“This measure was necessary because requiring our military to go into combat with only an IOU instead of pay would be a travesty,” Sen. Carl Levin (D-Mich.), chairman of the Armed Services Committee, said on the Senate floor Monday. “But don’t be fooled — it’s just one travesty among many. Even if we restrict our view to the impact of a government shutdown on the military, there are many other terrible impacts of a shutdown.”

About 400,000 Defense Department workers, approximately half of the department’s civilian workforce, have been exempted from furlough and will receive pay, according to the Pentagon.

Defense Secretary Chuck Hagel, who was traveling in South Korea, told reporters that Defense Department civilians who are exempt from the shutdown will remain at work and will be paid.

Adm. Bill Moran, chief of naval personnel, explains to military personnel and naval civilians Tuesday that federal government employees are to leave work early due to the government shutdown. (Marvin Joseph/The Washington Post)

“To think of what this is doing to these civilian employees and their families . . . they’ve taken furloughs already this year — administrative furloughs,” the secretary said. “Now we have legal furloughs. This is going to impact the future of a lot of our employees.”

House Armed Services Committee Chairman Howard P. “Buck” McKeon (R-Calif.) said Tuesday that the Defense Department had interpreted the previous day’s measure too narrowly. The bill was not meant to limit pay only to those designated as essential workers.

He said many defense employees are being furloughed unnecessarily.

“I believe the legislation provides you broad latitude and I encourage you to use it,” McKeon wrote in a letter Tuesday to Hagel.

Obama issued a video message Tuesday to the Defense Department workforce promising that his administration will “continue to work to address any impact this shutdown has on you and your families.”

He said DOD civilians and their families deserve “better than the dysfunction we’re seeing in Congress.”