Coons, meanwhile, during a nationally televised debate portrayed O'Donnell as an extremist more interested in clever sound bites than offering solutions to the problems confronting the nation.
O'Donnell, a tea party favorite, has drawn attention for her comments years ago that she dabbled in witchcraft as a teenager and opposed masturbation in a crusade against premarital sex. She frequently sought Wednesday to distance herself from her past views, softening her rhetoric on issues such as homosexuality and evolution.
"We're moving past that; were talking about the issues," O'Donnell said when asked by CNN anchor Wolf Blitzer why she had opened a recent television ad by declaring "I'm not a witch."
O'Donnell said the ad was meant to put to rest the controversy surrounding her past statements as a television commentator.
The Republican tried to shift the conversation to Coons' record of presiding over three property tax increases as chief executive of Delaware's largest county.
"My opponent has a history of promising not to raise taxes on the campaign trail and then breaking those promises as soon as he takes office," she said.
Coons, meanwhile, took several digs at O'Donnell, saying she had misrepresented his record while offering confusing answers to questions that were posed to her.
"I don't have any classified information about China or its plans," he said, referring to O'Donnell's assertion in a 2006 debate that China is planning to take over the U.S. and that she had received classified intelligence while working with a humanitarian group.
Wednesday night's debate at the University of Delaware pitted Coons, who excelled as a debater in Amherst College, against O'Donnell, who has appeared as a conservative pundit for years on TV talks shows such as Bill Maher's "Politically Incorrect."
O'Donnell has been in the spotlight since she stunned the state by beating Mike Castle, a congressman and former governor, in the GOP primary last month. She has been relentlessly parodied by comedians and others for some of her past statements.
O'Donnell provided a light moment when she chided Coons: "You're just jealous you were not on Saturday Night Live."
Coons quipped that he couldn't wait to see who would play him. In their first debate in the closely watched race, Coons and O'Donnell discussed their views on economic issues and health care reform but also offered sharply different positions on a wide variety of social topics.
The two disagreed on the military's "don't ask, don't tell" policy on gays serving in the military.
Coons said he would move swiftly to repeal it, calling the policy "discrimination, plain and simple."
O'Donnell, who in the past has described homosexuality as a social disorder, avoided a firm position but said the decision should be left to military leaders.
"Congress should not be forcing a social agenda onto the military," she said.
O'Donnell also refused to say whether she believes evolution is a myth, as she has said previously.
The Republican was stumped at one point when asked to cite a recent Supreme Court decision with which she disagreed, saying she couldn't come up with one "off the top of my head." She said she would respond later on her website.
Asked the same question, Coons cited the recent landmark Supreme Court decision making it easier for corporations and unions to spend money in elections.
"Corporations aren't really entitled to the same free speech rights, in my view, as people," he said.
Coons also addressed criticism from O'Donnell about a college newspaper column he wrote entitled "Chris Coons: The Making of a Bearded Marxist," that discussed his political transformation after seeing widespread poverty during a trip to Kenya. He said the headline was intended as humorous and that he's never been anything but a "clean-shaven capitalist." But O'Donnell said that the column and his tax increases show he has "Marxist beliefs."
O'Donnell said Obama and other Democrats are putting their weight behind Coons because "they see him as a rubber stamp for their agenda." She noted that Senate Majority Leader Harry Reid, D-Nev., has called Coons his "pet."
"I don't know why Harry Reid said that," Coons said. "I'm nobody's pet. I'm going to be a bulldog for Delaware."