When Senate Democrats gutted the filibuster for most nominations in 2013, they refused to touch the rules governing the Supreme Court — but some liberals are now starting to reconsider.

With President Barack Obama set to unveil his Supreme Court pick on Wednesday morning, and Republicans steadfastly refusing to even meet with the nominee, some Democrats — mostly hailing from the caucus's liberal wing — are openly entertaining the option of dumping the 60-vote threshold still needed to confirm nominees to the nation's highest court.

Sen. Brian Schatz (D-Hawaii) calls himself an institutionalist who doesn't "yet" support changing filibuster rules in light of the acrimonious Senate fight over replacing deceased Justice Antonin Scalia.

"But at some point, you have to ask," Schatz said in a recent interview. "What do all these institutional prerogatives mean if the institution not only can't do its own job, but is destroying the ability of other branches of government to do their jobs?"

Others are taking it one step further. Sen. Richard Blumenthal (D-Conn.) said he supports abolishing the filibuster for the Supreme Court altogether, a position that he says he has long held but a stance that is taking on new significance in this latest nomination battle.

Blumenthal, who has argued four cases before the Supreme Court and clerked for former Justice Harry Blackmun, argues that other federal judges have lifetime appointments and yet can be confirmed by a simple majority — and that same standard should be held for the Supreme Court.