On Wednesday, Mr. Marx’s group announced a campaign called #AnotherGreatJustice, which it described as a major national cable and digital ad buy. Other well-funded groups like the United States Chamber of Commerce plan to weigh in soon.

“This is a 10 out of 10 motivator,” said Leonard A. Leo, an informal adviser to the president on judicial nominations and a leading conservative judicial strategist, explaining how critical the courts have been for Republican voters, especially since the 2016 death of Antonin Scalia, a conservative icon. “Succession on the court, the possibility of multiple vacancies and appointments is something that’s been very much on the minds of the conservative movement.”

Mr. Trump has already appointed young and highly conservative appellate judges, making appointments at a faster rate than his predecessors. During his presidency, judicial confirmation fights have also become more partisan and polarized. The president’s judicial nominees have faced an average of 23 “no” votes each — which, according to the Pew Research Center, is by far the highest for any president since the Senate expanded to its current size of 100 members in 1959.

As mobilized as the right may be, Democrats have never faced a confirmation quite like this, with Roe v. Wade seemingly as imperiled as it has ever been. Though they may not have the Senate votes to block the president’s nominee, the energy that Democrats can create around the threat of abortion becoming illegal will most likely help level the playing field with the right, both in terms of intensity and money raised.

Within hours of Justice Kennedy’s retirement announcement, the Democratic Senatorial Campaign Committee had started a fund-raising campaign on social media and sent an email declaring, “This is an all hands on deck moment, team.” Senator Elizabeth Warren, Democrat of Massachusetts, sent out a fund-raising blast that told supporters that “women’s rights, equal rights, and health care are on the line.” Representative Beto O’Rourke, a Texas Democrat who is running for Senate against Ted Cruz, also emailed, “This couldn’t be more urgent.”