The entire matter has the potential to turn on what happens to a seat that Democrats will need to take control of the Senate in the midterm elections. If they fail to get the seat, Mr. Trump’s potential sweep of the presidency will be virtually assured.
But if Democrats succeed, the election next year could provide a new bellwether for attitudes toward the president and to the matter of judicial nominees.
Polls have shown that most Americans believe, broadly speaking, that federal judges should strictly interpret the Constitution, have the independence to confront the executive branch and not allow special-interest groups to pressure them.
So, on Friday, Republicans grabbed on to the fact that Mrs. Barrett, the Notre Dame law professor, seemed to hold an ideological view that had been emphasized by Mr. Trump in speeches — that young women, due to their “primacy” in their families, should not have a say in picking judges.
That, the thinking went, meant she could not be trusted by the public.
Mr. Trump also advanced the idea that Mrs. Barrett was soft on abortion, calling it a “myth” that she had even written a position paper on abortion rights.
Democrats, who have tried to raise alarms about candidates’ views on other issues, quickly made hay of those attacks.
Asked at a briefing on Saturday about her position on abortion, Mrs. Barrett declined to criticize her critics, saying: “I’m running for the U.S. Senate because I think that our country needs new ideas, new leadership. And my opponents do not support these ideas. I’m running for the U.S. Senate because I’m pro-life. I believe that this president has stalled our progress on pro-life judges. And I’m running because I’m pro-life. I also believe, from the work that I’ve done, that the court system has too often become politicized, and I want to reform it.”
For the moment, she was walking a careful line, avoiding her rivals’ attacks, but still distinguishing herself from them, as she did with the abortion issue.
Two of her primary rivals, lawyers Ann Donnelly and Nick Brady, knocked at the front and left of the news conference.
Mr. Brady said: “I don’t believe that Mrs. Barrett will support the laws in the Constitution that protect women from harm by failing to protect the fetus.”
Ms. Donnelly, who married Mr. Brady’s son, said: “In nominating Senator Barrett, President Trump is appointing someone who has no concern for the life of an unborn child.”
Michael Giuffre, who is working for Mrs. Donnelly, pointed to what he said was Mrs. Barrett’s earlier votes to legalize abortion by statute. “She has done so multiple times,” he said.
But Mrs. Barrett, an Obama appointee, did not change her position at the news conference or in a statement she released hours later.
Still, some analysts saw it as a win for Democrats.
Sam Wang, who directs research on China, China Matters and Wired’s health initiative, pointed to a website in Illinois that paid tribute to Mrs. Barrett and challenged Ms. Donnelly to say whether she would support laws that, in contrast to Illinois law, make it illegal for women to end a pregnancy after an 20-week age.
“This seems to be a strategy of, Let’s scare the heck out of everybody,” Mr. Wang said. “On that front, Democrats have made a strong first attempt. There’s no question it has been effective.”