Updated

Senate Democrats on Tuesday muscled through the confirmation of a key judicial nominee, in the first such vote since they weakened the chamber's filibuster rules and undermined the power of the minority party.

Senators voted 56-38 to approve Washington lawyer Patricia Millett to join the U.S. Court of Appeals for the District of Columbia, the nation's second most powerful court.

Amid objections from Republicans, the vote now sets the stage for a series of votes on nominees who otherwise could have had a tough time getting confirmed.

Both sides saw Millett's appointment as pivotal. It will give Democratic-appointed judges a 5-4 majority over those chosen by Republican presidents for that court, which rules on the legality of White House actions and federal agency regulations.

"I'm confident she will serve with distinction on the federal bench," President Obama said in a statement.

Until recently, it would have taken a coalition of 60 senators to advance Millett's nomination. But Majority Leader Harry Reid pushed through changes, to the dismay of Republicans, that would allow most judicial and executive nominees to advance and get approved with just 51 votes.

In Tuesday's vote, Sens. Susan Collins of Maine and Lisa Murkowski of Alaska were the only Republicans to join Democrats in supporting Millett.

The Senate then approved Rep. Mel Watt, D-N.C., to head the Federal Housing Finance Agency. During that vote, Democrats again took advantage of the weakened filibuster rules, voting 57-41 for Obama's pick to head the agency that oversees mammoth home mortgage lenders Fannie Mae and Freddie Mac, which own or guarantee about half of all U.S. mortgages. Two Republicans, Richard Burr, of North Carolina, and Rob Portman, of Ohio, voted with Democrats.

Republicans say Watt is unqualified to lead the agency. Democrats say Watt, a 21-year House veteran, has the necessary skills and is opposed by Republicans because they think he is too liberal.

Millett, the first nominee to emerge from the highly partisan filibuster fight, is a veteran who has argued 32 cases at the Supreme Court and has strong bipartisan credentials.

A Harvard Law School graduate, Millett served as an assistant to the solicitor general under President Bill Clinton, a Democrat, and President George W. Bush, a Republican. She then joined the Supreme Court practice at Akin Gump, one of Washington's biggest law firms.

Over the next two weeks, Democratic leaders also plan to win final Senate approval for two other Obama nominees to the D.C. Circuit, as well as his picks to head the Federal Reserve and the Department of Homeland Security.

Republicans responded furiously to the changes in the filibuster rules as they left for the Senate's Thanksgiving break and continued to rail against the changes on Monday.

As Reid asked for unanimous approval of 76 nominations -- including Janet Yellen to lead the Federal Reserve and Jeh Johnson, Obama's choice to run the Homeland Security Department -- Sen. Lamar Alexander, R-Tenn. rose to object.

"Who knows what the next power play will be?" Alexander said.

Reid said Alexander's objections were "as flat as a bottle of beer that's been open for six months." He then scheduled votes on several nominations.

Most of the nominees slowed by Alexander's objection were for minor posts, including some federal judges, lower-level ambassadors and government boards.

Reid planned to move ahead with votes on six key Obama nominees before the Senate adjourns next week -- Millett and fellow D.C. appeals court nominees Cornelia "Nina" Pillard and Robert Wilkins; Yellen and Johnson; and Watt.

Republicans retain options under Senate rules to slow but not stop presidential appointments by themselves. For appeals court and Cabinet-level appointments they can still make majority Democrats put off a final confirmation vote for up to 30 hours. For lesser posts like Watt's, the maximum is eight hours.

Republicans can also force at least one procedural vote on each nominee before roll calls are taken to end filibusters and for final approval. Each requires only a simple majority for Democrats to prevail.

Republicans have little criticism of Millett and Obama's other D.C. Circuit nominees. Instead, they've said they oppose adding judges to the court and tilting its balance when its caseload is smaller than other federal appeals courts.

The Associated Press contributed to this report.