Obama telephoned Sotomayor on Sunday to wish her good luck and congratulated her for having met with 89 senators before the hearings.
"The president expressed his confidence that Judge Sotomayor would be confirmed to serve as a justice on the supreme court for many years to come," a White House statement said.
Experts say the Democrats have the 60 votes needed to overrun any Republican efforts to use delaying tactics to block the nomination.
"I suspect she will be confirmed, but I would hope that it does not turn into a partisan fight for the good of the court," Patrick Leahy, a Democratic senator and chairman of the senate judiciary committee, said on CBS television.
"The strategy is to be as thorough as we can in examining her record, what she has said, and to conduct the hearings in a fair, impartial, and thorough way"
Jon Kyl, Republican senator
"She has a track record. She has shown to be a mainstream judge. You don't have to guess what kind of a judge she's going to be."
But Republicans have served notice they plan to put up a fight, giving one of their 14 witness slots to one of the white firefighters whose claim of racial discrimination Sotomayor rejected - only to have the supreme court reverse her ruling in late June.
Jeff Sessions, a Republican senator, raised doubts about whether Sotomayor could be objective, saying supreme court justices need to "do equal justice to the rich and poor alike".
"She has advocated a view that suggests that your personal experiences, even prejudices ... would influence a decision you make, which is a blow, I think, to the very ideal of American justice."
But senator Jon Kyl, reported to be leading the Republican strategy for the confirmation hearings, vowed on ABC that Sotomayor would get a fair hearing.
"The strategy is to be as thorough as we can in examining her record, what she has said and to conduct the hearings in a fair, impartial and thorough way - and then make our decisions."
Sotomayor's personal rise from a poor childhood in the Bronx in New York to the pinnacle of US justice mirrors Obama's own rise to power.
Upon announcing her nomination, Obama declared that Sotomayor could boast a "brilliant legal career" and "the wisdom accumulated from an inspiring life's journey".
Princeton-educated Sotomayor, who hails from a Puerto Rican family, would be the second woman currently on the court, alongside Justice Ruth Bader Ginsburg.