WASHINGTON — Democrats on Friday promised a swift confirmation process for Judge Ketanji Brown Jackson, celebrating President Biden’s pick for the Supreme Court as Republicans signaled that they had little appetite for a toxic battle over the first Black woman to be nominated for the post.

While Democrats and their progressive allies extolled Judge Jackson as a brilliant and qualified choice, many Republicans said her selection reflected the power of the “radical left” over Mr. Biden, underscoring the divisions that are certain to shape a confirmation process that has become as much about politics and ideology as judicial record and professional background.

Despite the disagreement, there were early indications that Judge Jackson’s review could avoid the kind of scorched-earth partisanship of recent Supreme Court fights. Given the historic nature of her nomination and the fact that she would not change the court’s 6-3 conservative tilt, leading Republicans did not seem inclined to engage in a bitter clash that they were almost certain to lose.

Even as he dismissed Judge Jackson as “the favored choice of far-left dark-money groups” and noted that he had opposed her confirmation in the past, Senator Mitch McConnell, the Kentucky Republican and minority leader, said he looked forward to meeting with her in person. It was a far cry from 2016, when he refused to sit down with Merrick B. Garland, President Barack Obama’s pick for the court, whose nomination he killed.

The uncharacteristically muted statements from Mr. McConnell and many others reflected Republicans’ concern about appearing overly aggressive in attacking the first Black female nominee.

Instead, Republicans seemed intent on showing that they would treat Judge Jackson with respect and conduct dignified proceedings, even though most are likely to oppose her confirmation. They said they were determined not to emulate the tactics of Democrats, who they say were unfair to Justice Brett M. Kavanaugh during his confirmation hearing in 2018, when allegations of past sexual misconduct were aired.

“No matter what,” said Senator John Cornyn, Republican of Texas and a senior member of the Judiciary Committee, “Judge Jackson will be given the dignity and respect she deserves. The American people will see a starkly different process from the treatment of Justice Kavanaugh and other judicial nominees during the previous administration.”

Top Democrats have said they would like the Senate to vote on Judge Jackson’s nomination by April 8, before a scheduled two-week recess. The process will begin in earnest next week, when she begins so-called courtesy meetings with Republican and Democratic senators. The fact that she underwent Senate review for her seat on the U.S. Court of Appeals for the District of Columbia Circuit less than a year ago should bolster the chances of sticking to that timeline.

But the conflict in Ukraine and Washington’s focus on it could potentially upset the plans and slow her consideration. In addition, one Democrat, Senator Ben Ray Luján of New Mexico, had a stroke last month and has been absent. Democrats will want all their members on hand for the final vote in case they are needed.

After they were informed of the nomination on Friday, Democrats and their liberal allies portrayed Judge Jackson, a federal judge since 2013, as an impeccable pick who would provide valuable experience as a former public defender. She would ensure that “the Supreme Court reflects the nation as a whole,” said Senator Chuck Schumer of the New York, the majority leader.

“To be the first to make history in our nation, you need to have an exceptional life story,” said Senator Richard J. Durbin, Democrat of Illinois, who as the chairman of the Judiciary Committee will preside over confirmation hearings, which are expected in late March. “Judge Jackson’s achievements are well known to the Senate Judiciary Committee, as we approved her to the D.C. Circuit less than a year ago with bipartisan support.”

Other Democrats said the fact that Judge Jackson was recently grilled by Republicans on the Judiciary Committee in winning her spot on the U.S. Court of Appeals was a significant advantage.

“She gave as good as she got in a very respectful and graceful way,” said Senator Richard Blumenthal, Democrat of Connecticut and a member of the panel. “She was just masterful.”

While Republican lawmakers mostly held their fire on Friday, party activists were out in force denouncing Judge Jackson within hours of her selection. The Republican National Committee called her a “radical, left-wing activist” and put out a document previewing the party’s line of attack, calling attention to a decision she made blocking an element of President Donald J. Trump’s restrictive immigration policy, her work as a lawyer on a brief filed by abortion rights groups and her membership in the Cosmos Club, a private institution it called a “club of the Washington elite.”

The Senate could confirm Mr. Biden’s Supreme Court nominee without a single Republican vote, but he and his party would like to avoid that if possible — and Judge Jackson has drawn some Republican support in the past.Even before the judge was chosen, the president and Mr. Durbin reached out to Republicans they saw as potentially open to supporting a Biden nominee, including Senators Susan Collins of Maine and Mitt Romney of Utah.

Mr. Biden called Ms. Collins again on Friday morning to personally inform her of his choice before he announced it publicly, according to a person familiar with the private conversation who discussed it on the condition of anonymity.

Democrats say that bipartisan backing for the nominee would help build her credibility and that of the court. They also hope that some Republicans will welcome the opportunity to support the first Black woman to join the Supreme Court and be willing to put aside ideological differences if they consider a nominee who is qualified for the job.

If all 50 Democrats back the nominee, at least one Republican vote would be needed to avoid the spectacle of Vice President Kamala Harris having to break a tie to seat a new justice, which would be a first in Supreme Court confirmation history.

But chances for a significant bipartisan vote appeared minimal.

In addition to Ms. Collins, Senators Lisa Murkowski of Alaska and Lindsey Graham of South Carolina were the only Republicans to vote for Judge Jackson when she was named to the appeals court in June.

While more Republicans could still decide to back her for the Supreme Court, it would be unusual for a senator who opposed a nominee for a lower court to then support her for a higher judicial position.

Mr. Graham — who had pressed for Mr. Biden to choose Judge J. Michelle Childs, a Federal District Court judge in South Carolina, for the vacancy — cast substantial doubt on Friday on his willingness to support Judge Jackson’s confirmation. Mr. Graham said on Twitter that her nomination “means the radical Left has won President Biden over yet again. The attacks by the Left on Judge Childs from South Carolina apparently worked.”

In an interview this month, Mr. Graham said he did not intend to “reward” progressive critics of Judge Childs by backing an alternative choice.

Ms. Murkowski and Ms. Collins have both shown a willingness to support the judicial nominees of Democratic presidents. Ms. Murkowski has new political incentive to do so: She is seeking re-election in Alaska under a new system and could benefit from the support of independents and Democrats who back Mr. Biden’s nominee.

Ms. Collins issued a statement on Friday in which she complimented Judge Jackson’s qualifications and suggested that she was undecided about how to vote.

“Ketanji Brown Jackson is an experienced federal judge with impressive academic and legal credentials,” Ms. Collins said. “I will conduct a thorough vetting of Judge Jackson’s nomination and look forward to her public hearing before the Senate Judiciary Committee and to meeting with her in my office.”

In addition to meetings with individual senators, the nominee and her support team will need to answer an in-depth questionnaire from the Judiciary Committee that seeks to create an exhaustive record on topics such as speeches, writings and past cases. At some point in the next few weeks, the nominee will also take part in mock hearings known as murder boards to practice responses to the sort of questioning anticipated from Republicans.

With the announcement of the nomination behind them, Democrats were enthusiastic about the hearings and confident of the outcome.

“I know Judge Jackson will be an excellent Supreme Court justice,” said Senator Debbie Stabenow, Democrat of Michigan. “What an exciting time for our country.”