As Sotomayor made her Senate debut with a series of private meetings with leading senators, Republicans said they would prefer holding hearings on her nomination in September, which could cloud the speedy summertime confirmation that Obama wants.
Sotomayor, who would be the high court's first Latina justice and its third woman, told senators she would follow the law as a judge without letting her life experiences inappropriately influence her decisions.
``Ultimately and completely, a judge has to follow the law no matter what their upbringing has been,'' Democratic Sen. Patrick Leahy, the Judiciary Committee chairman, quoted the nominee as saying in their private session.
Republicans are questioning how she would apply the law, noting her remark in 2001 that she hoped her decisions as a ``wise Latina'' would be better than those of a white male who had not had the same experiences. Obama has said she misspoke; some Republicans have called the comment racist.
Leahy, hoping to shepherd a smooth and quick confirmation for Sotomayor, asked her what she meant by her 2001 comment and said the judge told him: ``Of course one's life experience shapes who you are, but ... as a judge, you follow the law.''
Democrats praise Sotomayor's life story as the New York-born daughter of Puerto Rican parents who was reared in a housing project and went on to Princeton and Yale universities before ascending to the highest legal echelons.
``We have the whole package here,'' said Reid. ``America identifies with the underdog, and you've been an underdog many times in your life, but always the top dog.''
In the new poll, half said she should be seated on the court while 22 percent opposed her confirmation. About a third had a favorable view of Sotomayor while 18 percent viewed her unfavorably.
She was looked upon more positively than any of three Supreme Court nominees Bush put forward over four months in 2005: Chief Justice John Roberts, Justice Samuel Alito, and Harriet Miers, who withdrew from consideration.
Roberts, the most popular of the three in polling at the time, was supported for confirmation by 47 percent, and 25 percent had a favorable impression of him.
Democrats hope to begin the sessions next month, which would meet Obama's goal of having her confirmed before the Senate leaves in early August for a monthlong vacation.
Reid said while Democrats want to hold hearings ``as quickly as we can,'' they would not seek to impose ``arbitrary deadlines.''
He sidestepped questions about her past decisions, telling reporters that he never has read any of the hundreds she has written during her 17 years as a federal judge. And, he added, ``if I'm fortunate before we end this, I won't have to read one of them.''
Democrats hold 59 votes in the Senate, more than enough to win Sotomayor's confirmation, but short of the 60 it would take to advance the nomination should Republicans try to block it.
Democratic Sen. Dianne Feinstein asked Sotomayor about abortion, a hot-button issue on which she has not ruled, leaving interest groups on both sides wondering about her position.
Feinstein would not describe Sotomayor's response, saying she would rather the subject be discussed in open confirmation hearings with the nominee participating. Still, Feinstein hinted that she believed the judge would uphold abortion rights, established in the 1973 Roe v. Wade Supreme Court decision.
``She's a woman who is well-steeped in the law, and well-steeped in precedent, and I believe that she has a real respect for precedent,'' Feinstein said.
Associated Press writers Ann Sanner, Laurie Kellman and Ben Feller contributed to this report.