The one-star command, located at Fort Bragg, was created in 2018 to help sustain the Army's specialized units built to assist partner forces worldwide.
Justices were skeptical Monday that the case was an exception to other lawsuits against defense contractors, which usually get immunity in such litigation.
The government pulled together funds to pay troops Oct. 15 and now Nov. 1, but officials said it’s doubtful they'll be paid again if the shutdown persists.