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PURCHASE, N.Y. -- Hillary Rodham Clinton formally announced her campaign for the Senate on Sunday, the first such bid by a first lady in the nation's history.

President Clinton and their daughter, Chelsea, applauded as she promised to improve public schools, provide universal health care and bring jobs to New York. She moved to the state last month.

"I may be new to the neighborhood, but I'm not new to your concerns," Clinton told a crowd of 2,000 supporters and reporters at the State University of New York-Purchase.

Clinton emphasized her years working for children's concerns and women's rights.

"I care about the same issues you do. I understand them and I know we can make progress on them," she said. "That's why, my friends, I want to be your senator."

Clinton described herself as a "new Democrat. I don't believe government is the source of all our problems or the solution to them."

Clinton's race against New York Mayor Rudy Giuliani, a moderate Republican, promises to be as hard-fought as it is historic. A poll released Sunday shows Clinton and Giuliani in a statistical dead heat. Both campaigns have raised record amounts of money. And although they tend to agree on social issues like abortion rights, gay rights and gun control, each has portrayed the other as ideologically extreme.

On a day guaranteed to produce attention for Clinton, Giuliani appeared on five Sunday talk shows. Like Clinton, he cast himself as a fighter on issues and took a jab at her recent move to New York.

"My record of success comes out of my knowledge, experience, background and life experience as a lifetime resident of the state," he said on CBS's Face the Nation.

Giuliani hasn't scheduled a formal announcement, but when asked on ABC's This Week whether he planned to run, he said, "Looks that way."