With the Supreme Court nomination of Brett M. Kavanaugh completed, GOP senators are quickly pivoting to filling out the rest of the federal courts, eyeing more than 40 district and circuit judges they want to confirm before the end of the year.

One top priority is filling the seat left vacant on the powerful D.C. Circuit Court of Appeals when Justice Kavanaugh was elevated.

Senate Judiciary Committee Chairman Charles E. Grassley, Republicans’ point man on the issue, said if the White House can nominate someone this week, lawmakers could have Justice Kavanaugh’s replacement seated by Christmas.

That would be in addition to 38 district judges and three circuit judges already pending on the Senate floor, who Republicans say they should confirm before they leave Washington to campaign for the mid-term elections.

“McConnell ought to keep the Senate in session until we get all 41 of those judges done,” Mr. Grassley told conservative radio host Hugh Hewitt Wednesday.

The Judiciary Committee could add nine judges to that list during a meeting Thursday, and five others had their confirmation hearings Wednesday, meaning they, too, could see committee action this month.

“I think we will easily get through them by the end of the year. If not, we will be here Christmas Day,” Sen. John Kennedy, Louisiana Republican, told The Washington Times.

Filling out the courts with an army of conservative jurists has been a GOP project since the day Mr. Trump took office — and they’ve made historic progress.

In less than 21 months, the Senate has confirmed two Supreme Court justices, 26 circuit court judges and 41 district court picks.

The White House didn’t respond to a request for comment Wednesday on whether Mr. Trump will be able to meet Mr. Grassley’s hope of confirming a Kavanaugh replacement this year.

Democrats, though, laughed off the chances the GOP could move so quickly.

“That is the first I have heard of it. That would strike me as an ambitious schedule,” said Sen. Chris Coons, Delaware Democrat.

Nominations could be particularly tricky with the bad blood built up during the Kavanaugh confirmation process still weighing on senators.

He won confirmation Saturday on a 50-48 vote, surmounting near-total opposition from Democrats, who complained about his 12 years as a judge and cited uncorroborated allegations of sexual assault from Justice Kavanaugh’s high school days.

Republicans said Democrats harnessed the accusation in a partisan attempt to sink the nomination. Democrats say Republicans moved too quickly, refusing to release millions of pages of documents from the judge’s background and failing to fully investigate the assault allegation.

Nerves were still raw Wednesday, when the Judiciary Committee held a hearing on two nominees for the 6th Circuit Court of Appeals and three district court judges.

Both of the appeals court nominees are from seats allotted to Ohio, and Sen. Sherrod Brown, Ohio Democrat, testified against them, asking senators to reject them.

He objected to their past representation of clients on cases related to Ohio’s cleaning of its voter rolls and challenges to health care coverage for pre-existing conditions.

“Rather than granting these nominees lifetime authority to threaten Americans’ voting rights and health care, we should start over with two different candidates who can earn consensus,” he argued.

He also said he has declined to return his blue slip — a senatorial courtesy that gives home-state senators a chance to express acceptance of a nominee. Democrats say the committee shouldn’t move ahead without both home-state senators returning their blue slips.

“This is an affront to our traditions,” said Sen. Cory Booker, New Jersey Democrat. “I’m sad to see further erosion of this body’s critical institution traditions today.”

Republicans counter that the blue slip process is a courtesy that is taken into account, but home-state senators shouldn’t have an absolute veto over a president’s picks.

Sen. Mike Lee, Utah Republican, said he’s ready to work with Democrats to overcome the nastiness of the Supreme Court confirmation battle.

“We need to figure out how to fulfill our advice and consent role in a dignified manner,” Mr. Lee said.

The next test for Democrats will be how many of the 41 judges awaiting votes are granted floor time.

Senate Majority Leader Mitch McConnell, Kentucky Republican, is trying to work out an agreement on a package of nominees to be approved in the next week or so. The Senate would then adjourn until after the Nov. 6 elections.