It is widely expected that the administration will appeal with court's decision, which could very well make its way up to the Supreme Court.

Womack's bill would stay the NLRB's decision "until final disposition is made in certain actions relating to the appointment of individuals to such Board that are pending in Federal court."

"[T]he U.S. Court of Appeals for the D.C. Circuit's January decision gave us a basis on which to challenge the President's appointments, and this challenge must be resolved before the Board continues its work," Womack said. "That is exactly what my bill will do."

Republicans have previously blocked the nominations of Griffin and Block from going to the full Senate, and that of Richard Cordray to lead the Consumer Financial Protection Bureau. The Banking Committee will hold a hearing on Cordray's nomination on March 12th.

Of the five total slots on the NLRB, just three of them are filled now — by Block, Griffin and Chairman Mark Pearce. In recent weeks, Republicans have urged President Obama to nominate two Republicans to the board to fill the seats previously held by Brian Hayes and Terence Flynn.

There has been no recent indication from the White House as to when those appointments would be made and submitted to the Senate.

— This story was updated at 5:59 p.m.