URCHASE, N.Y. - Hillary Rodham Clinton made her Senate campaign official yesterday and, in a half-hour speech here before a stomping, screaming crowd of about 2,000, aimed to defuse her opponent's claim that she is ''ultraliberal'' and a ''carpetbagger.''
In a line that is likely to become a major theme of her campaign, she declared, ''I may be new to the neighborhood, but I'm not new to your concerns ... I care about the same issues you care about. I understand them. I know I can make progress on them.''
She then ticked off her positions on a host of issues - public education, health care, raising the minimum wage, bringing more jobs to upstate New York - starting each item with, ''I'm on your side'' and ending with ''that's why I want to be your senator.''
Throughout the speech, President Clinton sat behind her - along with their daughter, Chelsea, Hillary Clinton's mother, and a few of the state's Democratic leaders - but, maybe for the first time at a public political event, the president did not say a word.
He and Chelsea gave her a long hug - greeted by a storm of applause and blinding flashbulbs - after the speech was over.
Mayor Rudolph W. Giuliani, the as-yet-undeclared but apparent Republican candidate, was determined not to surrender the day to Clinton altogether. He appeared on all five national network political talk shows yesterday morning, touting his achievements and criticizing what he called her lack of them.
Clinton devoted much of her speech to rebutting the assertion that she has never accomplished anything.
An 18-minute documentary shown to the crowd before she stepped onto the stage noted her activism for children's causes as a lawyer 30 years ago, her experience as a staff member on the Senate committee that impeached Richard Nixon, her work on education and health reform in Arkansas and Washington, and her advocacy of women's rights in Beijing.
In the film, her mother remembers that as a child, Hillary ''was able to play with the boys and earn their respect'' - implying that she'll do the same in the male-dominated Senate.
Dr. T. Berry Brazelton, the famous pediatrician, says on camera, ''I don't endorse politicians ... but I can honestly say Hillary Clinton is my hero.''
At the same time, in her speech, Clinton dismissed the notion - which some of Giuliani's fund-raising letters have alleged - that she is an old-fashioned liberal.
''I'm a New Democrat,'' she stated, echoing her husband's appeals when he first ran for president. She cited her belief in balanced budgets, welfare reform, and more police on the streets.
She never mentioned Giuliani directly, but she clearly had him in mind when she said, to much applause and laughter, that she would fight against ''the divisive politics of revenge and retribution.''
She also spoke out against school vouchers, which Giuliani supports.
Curiously, the two candiates disagree on very few issues - both support abortion rights, gay rights, and gun control - so they are likely to emphasize as dramatically as they can their areas of dispute.
Polls released in the past few days show her trailing Giuliani statewide by 3 to 7 percentage points - a virtual tie, given the statistical margin of error.
She is strongest in New York City, where Democrats outnumber Republicans 5 to 1, and among African-Americans, Hispanics, households with union members, and the poor.
Giuliani is strongest in the suburbs and among white people - including, to the surprise of many Democrats, white women.
This week, Clinton carries her campaign to the big upstate cities - Buffalo, Rochester, Syracuse, and Albany - which, many analysts believe, she must carry decisively in order to offset Giuliani's edge in the state's rural regions.
Yesterday's speech was broadcast live on some New York television stations, and, according to her campaign spokesmen, was transmitted to about 600 families across the state that were hosting fund-raising events attended by 25,000 people.
The race is likely to be one of the most heated - and expensive - in the country. Clinton has raised $8 million, Giuliani nearly $12 million.
