The Federal Circuit Court of Appeals decided Friday that these two recess appointments violated the Constitution because they were made when the Senate was not in recess. That decision immediately raised questions about the validity of the more than 200 NLRB decisions made since the appointments were made, and whether a similar challenge might be raised against an appointee to the Consumer Financial Protection Bureau.

The NLRB said on Friday that the court decision only applied in the context of one NLRB decision that was challenged by Noel Canning, a Washington State canning company. NLRB Chairman Mark Pearce said the NLRB believes Obama's appointments would be upheld in an appeal to the Supreme Court, and said the ruling would not stop the NLRB's work in the meantime.

Alexander rejected that, and said the NLRB should not be allowed to continue operating with Block and Griffin on the board.

"A new sign needs to go up at the National Labor Relations Board. Take down the sign that says 'open for business,' put up a sign that says 'help wanted, nominations accepted,' " he said.

Alexander also noted that because the NLRB now has just one Senate-appointed member — Pearce — the entire agency should be prevented from making rulings related to union rights. "The board should not be open for business," he said.