Senate Republicans on Thursday blocked a second of President Obama's nominees -- Patricia Millett to the U.S. Appeals Court for the Washington, D.C., Circuit.

Millett's nomination failed to clear a procedural hurdle after Republicans voted against bringing her nomination to a vote.

The Senate voted 55-38 to proceed with a vote on Millett's nomination -- shy of the 60 votes needed. Three senators voted present.

Minutes before, Republicans also blocked the nomination of Rep. Mel Watt (D-N.C.) to head the Federal Housing Finance Agency.

The combination of the two rejections -- and several contentious nominations in the days ahead -- has led some Democrats to suggest changing the chamber's rules. Shortly after the votes Thursday, Sen. Patrick Leahy (D-Vt.) said it's time to look at that option.

Republicans opposed Millett's nomination because they feared it would tip the balance of power on the D.C. Circuit court, which is  generally thought to be the second most important court in the country, behind the Supreme Court. The GOP also argued that the circuit court's small caseload didn't require a swift confirmation.

White House press secretary Jay Carney accused the GOP of obstruction. He called Millett “extraordinarily qualified” and said the arguments some Republican senators have made about the court's small caseload are “astoundingly hypocritical.”

“At this point, we would simply like to see our nominees confirmed – our highly qualified nominees confirmed,” Carney said.

Leaving the U.S. Capitol shortly after the Watt and Millet votes, Vice President Biden told reporters "I think it's worth considering" changes to the Senate filibuster rules.

Senate Majority Leader Harry M. Reid (D-Nev.) said he didn't know whether the Senate would reconsider Millett's nomination.

Updated at 1:41 p.m. Ed O'Keefe contributed to this post.