Without that third chair being filled, the board will be forced to shut down, unless President Obama makes recess appointments to keep the board running. And he has the constitutional authority to do so without congressional approval if the Senate is not in session. A President generally makes recess appointments when he is aware that his nomination does not have the necessary 60 votes to beat a filibuster.
Therefore, Senate Republicans hope their “gaveling in gaveling out” every few days, in order to not officially adjourn for the year, will block any such recess appointments.
Just before Christmas, Republicans warned President Obama in a letter not to make appointments to the NLRB without congressional approval:
Appointments to the NLRB have traditionally been made through prior agreement of both parties to ensure that any group of nominees placed on the board represents an appropriate political and philosophical balance. Indeed, the very statutory design of the Board is meant to ensure a basic level of bipartisanship in the appointment of Members. As you are undoubtedly aware, appointments to Board that depart from this tradition have resulted in some of the most contentious, divisive struggles we face in the Senate. Your controversial recess appointment of NLRB Member Craig Becker is an example of an NLRB nominee having been appointed over the objection of the Senate and the result of that decision has been unending controversy throughout Member Becker’s entire term on the Board, which has undermined the credibility of the entire NLRB.