Chuck Hagel’s halting and unconvincing appearance Jan. 31 before the Senate Armed Services Committee hardened Republican opposition to his confirmation, but his critics would likely have to mount an unprecedented, and very divisive, challenge to block him from becoming Defense secretary.

Since Hagel appears to enjoy the support of most, if not all, Democrats, Republicans would have to filibuster his nomination — something that has never been done to a Cabinet nominee since the advent of the 60-vote threshold nearly four decades ago, according to Senate records.

Several Cabinet nominees have failed to win the backing of a majority of senators — and others have withdrawn their names before reaching the Senate floor — but a filibuster would mark a serious breach in the unwritten protocol that governs the Senate. Such a challenge could also disrupt the deal reached last month between Democratic and Republican leaders to overhaul the filibuster.

No Republicans have said yet that they will demand Hagel clear that 60-vote hurdle, but the possibility has been bubbling below the surface in the Senate in recent days.

An aide to Senate Minority Whip John Cornyn of Texas, who has been among the most vocal opponents of Hagel’s nomination, said Feb. 1 that “all options are on the table.”