"I came into this thinking I have to work twice as hard as anybody else," she said. "I am an unconventional choice."
But Kennedy said there are "many ways to public service" and her accomplishments as a writer, mother and fundraiser for New York City public schools prepared her well for the post.
Kennedy sat down to talk with the AP at the Gee Whiz diner in lower Manhattan after weeks of avoiding the media. She seemed relaxed, eating a grilled cheese and bacon sandwich with coffee during the half-hour interview.
Kennedy's name first surfaced as a possible replacement for Sen. /*Hillary Rodham Clinton*/ in early December after President-elect /*Barack Obama*/ nominated Clinton to be secretary of state.
The Senate appointment rests solely with Democratic Gov. David Paterson, who has said he will wait until the Senate confirms Clinton as secretary of state before picking a successor.
Since Kennedy expressed interest in the job, she has faced sometimes sharp criticism that she cut in line ahead of politicians with more experience and has acted as if she were entitled to it because of her political lineage. More than a half dozen other elected officials are vying for the seat, including New York Attorney General Andrew Cuomo and several members of Congress.
Kennedy had spoken publicly about her interest in the seat only briefly, once on a swing through upstate New York and later in Harlem with the Rev. Al Sharpton.
She told the AP on Friday that she had been reluctant to appear to be campaigning for the job because it was an appointment, not an election.
"I was trying to respect the process. It is not a campaign," she said.
She also said she believes her approach had been "misinterpreted."
"If I were to be selected," she said, "I understand that public servants have to be accessible."