But her confirmation is not assured. Democrats have 59 votes in the Senate, one short of the 60 needed to overcome a filibuster.
This gives Republicans just enough room to put up a fight against the nominee, should they choose to.
The outcome of the still-undecided Minnesota Senate race could give the Democrats a filibuster-proof 60 votes by the time the Senate moves to a final vote on Sotomayor, if Al Franken, who is leading in the contested election, is ruled the winner.
But Republican Norm Coleman would have the option to appeal a Franken victory, and Republicans have been pushing him to leave the option open. If Sotomayor's nomination fight intensifies, Coleman could be encouraged further to seek an appeal.
Though Republicans reacted cautiously to Tuesday's announcement, 11 current Republican senators voted against Sotomayor when she was nominated to the appeals court by President Clinton in 1998. They included Kentucky Sen. Mitch McConnell, now the Senate Republican leader, and three senators on the current Judiciary Committee.
It's unclear how much resistance those Republicans will put up this time around. Sen. Chuck Grassley, R-Iowa, who voted against Sotomayor in 1998 and now sits on the Judiciary Committee, said in a statement that her appointment requires a "thorough vetting."
"We need to ask tough questions to learn how this individual views the role of a Supreme Court justice," Grassley said.
McConnell offered a similar outlook. Sen. Jim DeMint, R-S.C., though, said some of Sotomayor's "writings seem to raise serious questions about her approach to the Constitution and the role of the federal judiciary."
He added, "But I will withhold judgment."
Sen. Arlen Specter, who recently switched from Republican to Democrat, said when he switched that he would not "be an automatic 60th vote."
However, he released a statement Tuesday praising Sotomayor, saying "her confirmation would add needed diversity."
Franken, showing confidence, also released a statement saying he looks forward to joining his colleagues in examining Sotomayor's record. He called her a "remarkable jurist with an impressive record of accomplishment and a life story with which working families can identify."
Ultimately, it could be politically difficult for many Republicans, particularly those in Southwestern states, to lead a hard charge against a nominee who would become the first Hispanic Supreme Court justice.
A senior Democratic Senate aide told FOX News: "She's going to be confirmed with more than 60 votes."
The aide said Senate Republicans appear to be less critical of Sotomayor than some conservative groups.
"Groups will hit this hard. It helps with fundraising, but Senate Republicans don't really appear to have the appetite right now," the aide said.
The confirmation process is expected to take between 60 and 80 days. But Sen. Jeff Sessions, R-Ala., ranking Republican on the Judiciary Committee, has suggested 60 days might be needed just to prepare for the hearings.
He has said it might be better to hold the hearings in September. Majority Leader Harry Reid, D-Nev., and Judiciary Committee Chairman Patrick Leahy, D-Vt., have taken pains not to antagonize Republicans, so neither has pushed for an accelerated timeline.
But they likely will work hard to meet Obama's confirmation deadline of before the August recess, which begins the second week of that month.
FOX News' Trish Turner contributed to this report.