When Jeanine F. Pirro, the Republican district attorney from Westchester County, announced her decision this week to try to topple Hillary Rodham Clinton, the Democratic senator from New York, her battle cry was this: Do not let Mrs. Clinton fool you, she really wants to be president.

Ms. Pirro was raising an issue that has come up frequently in New York - a state that has produced more than its share of presidential candidates - and one Mrs. Clinton has faced before. But if history is any guide, New Yorkers tend not to worry much about voting for politicians viewed as having grander national ambitions.

In one example, voters knew that Robert F. Kennedy had hoped to be President Lyndon B. Johnson's running mate before he chose instead, in August 1964, to seek a Senate seat from New York. Though Mr. Kennedy, like Mrs. Clinton, faced questions on the campaign trail about being a carpetbagger (he spent much of his childhood in the Bronx but had a Virginia address just weeks before announcing; Mrs. Clinton is a native of Illinois), he won the seat and seemed to suffer no backlash when he threw his hat into the presidential ring in 1968.

Still, Ms. Pirro's offensive seems to be sticking, said Kieran Mahoney, one of her political advisers. He said Democrats "clearly feel that Pirro is hitting home because of their actions," which he said included Bill Clinton's recent recital, in a television interview, of a family rule: Do not look past the next election or you might not get past the next election.

In the long run, though, several political analysts said that of all the complaints voters might have about Mrs. Clinton, her potential presidential aspirations were not likely to be high on the list. Two recent polls on whether Mrs. Clinton should pledge to fulfill the full six-year term she is seeking achieved contradictory results. Several New York governors won presidential nominations in the first half of the 20th century. Theodore Roosevelt and his cousin Franklin gained the White House.