Obama advisers said they expected Mr. Biden to be a stronger and wilier point man for attacking the Republican ticket than John Edwards proved to be as the Democrats’ vice-presidential nominee in 2004, or Joseph I. Lieberman was as the running mate in 2000.

A task for Mr. Biden, the advisers said, will be to doggedly portray the presumptive Republican nominee, Senator John McCain of Arizona, as a handmaiden for President Bush who would continue his policies. In the words of one adviser, Mr. Biden can be an artful critic because he knows “chapter and verse” about Mr. McCain’s Senate votes and controversial positions after serving with him for two decades.

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The campaign also wants Mr. Biden to take a lead role in warning voters about possible McCain nominations to the Supreme Court. Given Mr. Biden’s history overseeing the confirmation hearings for Robert H. Bork and Clarence Thomas as chairman of the Judiciary Committee, advisers to Mr. Obama say he is well suited to argue that one or two nominations by Mr. McCain could result in rulings that outlaw abortion rights.

Mr. Biden’s addition to the ticket was cheered by many Democratic interest organizations. But some women’s rights leaders, in addition to some supporters of Mr. Obama, complained privately that Mr. Biden was not terribly inspiring and would do relatively little to woo women who support Mrs. Clinton and have yet to embrace Mr. Obama.

Some of these Democrats said that Mr. Biden was an inferior choice to Mrs. Clinton and that they were left cold by the selection of a 65-year-old white man. They recalled bitterly that he was not a forceful ally of women’s groups, and they were critical of his handling of Anita Hill during Justice Thomas’s confirmation hearings in 1991.

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Asked if the choice of Mr. Biden would win over supporters of Mrs. Clinton who remain undecided, Guy Cecil, who was political director of her campaign, said, “By the first week of November, her voters will recognize that the choice is too stark and the stakes are too high to vote for John McCain.”

The McCain campaign sought on Sunday to exacerbate tensions between the Clinton and Obama camps by running a television advertisement, “Passed Over,” which noted that Mrs. Clinton won millions of votes but was not chosen by Mr. Obama as his running mate because, the spot asserts, she spoke the “truth” during the primaries about his lack of “specifics” and “answers” to the nation’s problems.

A Clinton spokeswoman denounced the advertisement as misleading. McCain advisers said that they would keep running it and that they planned to criticize Mr. Biden as a Washington insider prone to gaffes and at odds with Mr. Obama’s message of changing the political status quo.

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Obama advisers said internal campaign polling did not suggest that Mr. Biden, a native of Scranton, Pa., could single-handedly deliver a particular state or voter demographic. But they expect to reap rewards in swing states like Iowa, Nevada and New Mexico from his popularity among retirees, veterans, Catholics, Jews and blue-collar voters.

“I spoke with one supporter in Dubuque, Iowa — a very Catholic, working-class city — who said that people were pulling out their old Biden yard signs and putting them on their lawns on Saturday,” said David Wilhelm, an Obama adviser who managed Mr. Biden’s Iowa operation in the 1988 presidential race and advised him when he briefly ran again this year.

Mr. Biden spent Sunday preparing for the campaign at home in Wilmington, Del., and getting to know his new senior staff.