Senate Republicans have blocked the confirmation of two of President Obama's nominees, setting the stage to reopen a bitter fight over the role of Senate filibusters and a president's prerogative on executive and judicial nominations.

The nomination of Patricia Millett to the U.S. Court of Appeals for the District of Columbia, which is seen as the nation's second-highest court, was blocked by a vote of 55 to 38. The confirmation vote for Rep. Mel Watt, D-N.C., to lead the Federal Housing Finance Agency also fell short, 56 to 42. Under Senate rules, both nominees required 60 votes to break a Republican filibuster.

The fight on the Senate floor today signaled a return to the bitter partisanship that nearly paralyzed the Senate earlier this summer before a handful of Republicans agreed to join Democrats in approving the president's nominees. The battle has deep implications for future nominations and administrations, with Senate Majority Leader Harry Reid once again considering changing Senate rules and traditions for filibusters.

Vice President Joe Biden expressed his outrage at the filibuster and suggested it was time to explore a serious change in Senate rules. The rules are designed to protect the minority party. "I think it's worth considering," Biden told ABC News. He added, "I think it's time for some common sense on confirmations."

Biden, who was in the Capitol to preside over the swearing-in ceremony for the newest Democratic senator, Cory Booker of New Jersey, said he was "very disappointed" at the nominees being blocked by Senate Republicans. Republicans did not resist Millett's appointment to the bench because of her ideology or judicial temperament, but rather because it would tip the balance of power on the prominent federal appeals court that is often the last stop before the Supreme Court. Republicans argued that the caseload did not require another judge.

"Our Democratic colleagues and the administration's supporters have been actually pretty candid," said Senate Minority Leader Mitch McConnell, R-Ky. "They've admitted they want to control the court so it will advance the president's agenda."