Will Republicans shut down the NLRB?

We know after New Process Steel the NLRB has to have 3 members to have a quorum. We also know Member Becker's recess appointment expires when Congress adjourns at the end of the year. Unless there is a confirmation or another recess appointment the NLRB will only have 2 members when Becker's appointment expires. Now some Republicans are urging Member Hayes to resign before the Board can implement controversial changes to the election process used to determine whether workers can unionize their employer's workplace. I think it is very likely Congressional gridlock will prevent the NLRB from having a quorum until some point after the 2012 election.