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If confirmed, the federal appeals court judge from New York’s 2nd Circuit would replace retiring Justice David Souter and would be only the third female justice in history.

Justice Ruth Bader Ginsberg is now the only female member of the court and is expected to retire in the near future because of pancreatic cancer.

The president called on the Senate to confirm Judge Sotomayor “as swiftly as possible.” He said he wants to have his pick confirmed or close to confirmation before Congress leaves Washington in early August for its annual month-long recess. That leaves lawmakers less than 60 days to make progress.

But Republicans have said they may try to prolong the process further, while still seeking to confirm Judge Sotomayor in time for the fall term, which begins in October.

Republicans reacted cautiously to the nomination, saying they look forward to learning more about the nomination.

“Senate Republicans will treat Judge Sotomayor fairly. But we will thoroughly examine her record to ensure she understands that the role of a jurist in our democracy is to apply the law evenhandedly, despite their own feelings or personal or political preferences,” said Senate Minority Leader Mitch McConnell, Kentucky Republican.

Mr. Obama, who taught constitutional law at the University of Chicago, chose Judge Sotomayor, the child of natives of Puerto Rico who was raised in a Bronx public housing project, over several other accomplished female jurists and attorneys.

Elena Kagan, the U.S. solicitor general, and Diane P. Wood, a judge on the U.S. Court of Appeals for the 7th Circuit, were considered seriously by the White House.

Sen. Byron L. Dorgan, North Dakota Democrat, said on MSNBC’s “Morning Joe” it was a good pick.

“I would expect some very interesting hearings, but I would expect her to be confirmed,” he said.

Though Judge Sotomayor graduated from some of the best schools with high honors, she has faced questions from the left about whether she will bring the intellectual firepower needed to counter conservative heavyweights on the court such as Chief Justice John G. Roberts Jr. and Justice Samuel A. Alito Jr., who were nominated by President George W. Bush.

Conservatives, meanwhile, are certain to highlight Judge Sotomayor’s role in upholding a lower court’s ruling that 20 New Haven, Conn., firefighters — 19 of them white and 1 of them Hispanic — could not reverse their local government’s decision to throw out two promotional exams because no black firefighters passed the tests.

The case — Ricci, et al. v. DeStefano, et al — is under review by the Supreme Court.

But the president’s pick ensures Democrats will continue to build broad support in the growing Hispanic-American electorate, a key voting bloc that both political parties see as up for grabs.

Mr. Obama said frequently in the days leading up to his announcement that he was not focused on gender and ethnicity as much as on whether a potential justice would interpret the law with “a common touch” and with “empathy.”

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