Senate Republicans blocked another of President Barack Obama’s picks for one of the nation’s top courts Tuesday, the latest skirmish in a nominations battle that has intensified partisan tensions in the chamber.

Tuesday’s near-party line vote derailed Obama’s selection of Georgetown University law professor Cornelia Pillard to fill one of three vacancies on the U.S. Court of Appeals for the District of Columbia Circuit. The vote was 56-41 in favor of ending GOP procedural delays that have blocked Pillard from winning confirmation — four short of the 60 votes Democrats needed.

The D.C. circuit court is considered one of the nation’s most powerful because it rules on administration orders and regulations and because some of its judges ultimately become Supreme Court justices. The D.C. circuit’s eight current judges are divided evenly between Democratic and Republican nominees.

Democrats used the vote to assail Republicans for opposing female nominees to the D.C. circuit. Republicans have blocked votes on two other Obama nominees to the same court this year, attorneys Patricia Millett and Caitlin Halligan.

“Women are grossly underrepresented on our federal courts. So what kind of message are Senate Republicans sending by refusing to even allow a vote on three of the most qualified female attorneys in this country,” Senate Judiciary Committee Chairman Patrick Leahy, D-Vt., said.

Iowa Sen. Charles Grassley, top Republican on the Judiciary panel, called such arguments “offensive,” adding that Democrats’ “last line of defense is to accuse Republicans of opposing nominees based upon gender or race.”

Democrats have been threatening that if Republicans continue derailing Obama’s nominations, they might unilaterally rewrite Senate rules to make it harder for the chamber’s minority party to do that. It is unclear that Democrats have enough votes to do so, with some senior lawmakers warning that the change would boomerang against them should the GOP recapture the Senate majority and the White House.

Susan Collins of Maine and Lisa Murkowski of Alaska were the only Republicans to join the Senate’s 54 Democrats in voting to move ahead the nomination.