She also said at a conference in 2005 that a “court of appeals is where policy is made,” a statement she seemed to understand at the time would be controversial, because she added, “I know this is on tape and I should never say that, because we don’t make law.” The White House said she meant that appeals courts play a greater role in interpreting laws than district courts, but Republicans pointed to the comment as another sign that she would try to impose her values in rendering decisions.

“Judge Sotomayor is a liberal activist of the first order who thinks her own personal political agenda is more important than the law as written,” said Wendy E. Long, counsel to the Judicial Confirmation Network, a conservative group. “She thinks that judges should dictate policy and that one’s sex, race and ethnicity ought to affect the decisions one renders from the bench.”

Other conservatives said they would focus on her ruling in a New Haven affirmative action case or on how she might rule on same-sex marriage. “Abortion is in some sense a stale issue that has been fought over many times, but gay marriage is very much up for grabs,” said Curt Levey, executive director of the Committee for Justice, a legal group. “Gay marriage will be bigger than abortion.”

As she was nominated on Tuesday, Judge Sotomayor did not retreat from her view that judges ought to look at the impact of their rulings. “I strive never to forget the real-world consequences of my decisions on individuals, businesses and government,” she said.

While conservative groups took aim, Republican senators responded more cautiously, weighing how aggressively they want to fight her confirmation. Twenty-nine Senate Republicans voted against her confirmation to the appellate bench in 1998, including Mitch McConnell of Kentucky, now the party’s Senate leader, while 25 voted for her. Of those still in the Senate, 11 voted against her and 9 for her.

Mr. McConnell said on Tuesday that the Senate would not be a “rubber stamp” and promised that Republicans would “examine her record to ensure she understands that the role of a jurist in our democracy is to apply the law even-handedly, despite their own feelings or personal or political preferences.”