The Senate confirmed another of President Trump’s appeals court nominees Thursday and advanced a slate of judicial picks through committee, even as the White House announced a list of still more appointees it wants to see sped on the federal courts.

As legislating begins to stall ahead of November’s elections, judicial nominations are taking up an increasing amount of senators’ time — and sparking ever-bigger rows between Democrats and Republicans.

Thursday’s big floor fight was over Michael Brennan, Mr. Trump’s pick to a seat on 7th U.S. Circuit Court of Appeals.

He was confirmed on a 49-46 vote over the objection of Democrats who said the GOP was upending longstanding Senate traditions in order to force the president’s picks onto the courts.

In this case, Sen. Tammy Baldwin, Wisconsin Democrat, said she never returned her “blue slip” signifying acquiescence in Mr. Brennan, who is from her home state. She said the president also ignored recommendations of a bipartisan state commission that vets judicial nominees.

Democrats said it was “an abject breach of senatorial courtesy” to ignore Ms. Baldwin’s objections.

But Republicans said the blue slip tradition isn’t a binding rule — and in fact for most of the last 100 years was treated as advisory.

Mr. Brennan’s confirmation followed a Wednesday vote confirming Kurt Engelhardt for a post on the 5th Circuit.

Senators will also vote Monday and Tuesday on four other circuit court nominees, which would give Mr. Trump 21 new circuit appointments since his inauguration. He’s also won confirmation of a Supreme Court justice and 17 lower district court nominees.

“I think the Republicans are processing nominations with speed that I have never seen before in 25 years,” said Sen. Dianne Feinstein, the top ranking Democrat on the Judiciary Committee.

President Obama at this point had just 20 judges confirmed — nine for the appeals courts and 11 for district courts.

Majority Leader Mitch McConnell, Kentucky Republican, has said he will prioritize judicial confirmations even over legislation on the floor because the judges will shape the country for decades to come.

He began this week vowing to get six nominees done.

Instead, he got two — but set up the votes early next week, after senators decided they wouldn’t stay through the weekend.

“They are just rolling them out. This is a real effort to stack the appellate court, there is no question about that,” Ms. Feinstein said.

Republicans, though, said the process is still not moving fast enough.

“Unnecessarily slow,” said Sen. John Kennedy, Louisiana Republican and member of the Judiciary Committee, who urged the chamber to stay in longer to get more people through.

“I’ve argued for a while that the best way to break the logjam is to work more hours,” he said. “Not all my colleagues agree with me, and I understand that’s because they want to go back to their districts, but we can sit around and complain and hope that it changes or we can do something about it and I think we ought to work weekends. I think if we do that will generate a little more cooperation.”

The Judiciary Committee on Thursday did advance Mark Jeremy Bennett, a nominee to the 9th Circuit. He cleared on an 18-2 vote, with two Republicans, Sens. Ted Cruz of Texas and Ben Sasse of Nebraska, voting “No.”

Mr. Cruz objected to Mr. Bennett’s move as Hawaii attorney general to back a too-limited interpretation of the Second Amendment’s right to bear arms.

The committee also voted unanimously to clear three district court nominees. Those include: Nancy E. Brasel for the District of Minnesota, Robert R. Summerhays for the Western District of Louisiana and Eric C. Tostrud for the District of Minnesota

Mr. Trump also said he’ll nominate an Idaho lawyer, Ryan D. Nelson, to another seat on the 9th Circuit, and announced a slate of nine others for district court spots.

Committee Chairman Chuck Grassley said he thinks the Senate can confirm Mr. Trump’s pending circuit nominees by the November election, but said it may be tougher to get the district court picks done.

“There’s about 30 district court people on the agenda right now, and I have pleaded with McConnell to work nights, to work Saturdays and weekends, and put the pressure on the Democrats,” the Iowa Republican said on the “Hugh Hewitt Show.”

He even suggested canceling one of the Senate’s scheduled vacations to get it done.

“Otherwise, all the hard work I’m doing in committee is for naught,” he said.