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Delaware Senate candidate Christine O'Donnell, the overnight sensation who despite new-found political fame has been unable to close the gap in polls, came out with guns blazing but launched a couple duds at a must-impress debate Wednesday night.

Several of O'Donnell's blanching assaults against New Castle County Chief Executive Chris Coons hit their target, but the Republican candidate shot blanks on a couple occasions when asked to provide specific answers to the moderator's questions.

In heated exchanges, O'Donnell accused Coons of cutting off low-income seniors and disabled people from a property tax exemption; of using a family company to secure stimulus funding; of being a "rubber stamp" for President Obama and Senate Majority Leader Harry Reid, who once enthusiastically described Coons as "my pet"; and of becoming a member of the Democratic Party only after receiving mentorship from a professor who was an avowed Marxist.

"I would argue that there are more people who support my Catholic faith than his Marxist beliefs," O'Donnell said.

But the cheery GOP nominee was often on defense as she answered questions about her personal financial problems and endured snide and dismissive mocking from her clear-spoken opponent.

O'Donnell, given an opportunity to define herself and her views before an electorate polls suggest are not convinced of her qualifications, used the stage at the University of Delaware to criticize "Obamacare" and the stimulus bill.

She stumbled on a question about her least favorite Supreme Court opinions. And at one point she jokingly accused Coons of being "jealous" he wasn't parodied on "Saturday Night Live."

Asked about a controversial Supreme Court decision that rolled back campaign finance restrictions, O'Donnell complained instead about the Democrats' so-called "Disclose Act," a campaign finance bill that has not passed Congress.

Both candidates frequently exchanged barbs at the debate.

"Ms. O'Donnell has experience at running for office, but not at really running anything," said Coons, "at delivering catchy slogans, but at not delivering on any real solution, and, frankly, at sharpening the partisan divide, not at bridging it. She is focused too little on the issues that really matter to Delawareans and too much on the issues that make for good sound bites."

O'Donnell tried to cast Coons as part of the old guard of politicians.

"At a time when he brags about balancing the budget by raising our taxes," O'Donnell said of Coons, the current New Castle County Executive, "we've got to ask: Do we want to send this gentleman to Washington, D.C.? I would say no. He's a career politician who has proven he knows how to play the 'I'll scratch your back, you scratch mine' game."

Seated a few feet apart at a circular table, Coons and O'Donnell riveted a packed hall of students, teachers, and administrators at the University of Delaware. The candidates responded to questions from moderators Wolf Blitzer of CNN and Nancy Karibjanian of Delaware First Media, as well as queries posed by students that were videotaped earlier on campus. And at times, the candidates directly questioned -- and testily interrupted -- each other.

When Coons touted the Triple-A bond rating that New Castle County has enjoyed under his stewardship, O'Donnell challenged him: "You inherited that good rating," she said. Coons shot back that such assessments are reviewed and reaffirmed periodically, before adding: "Ms. O'Donnell's not familiar with how bond ratings work."

Polls in the race show Coons has opened up a commanding lead over O'Donnell among likely voters. A Fox News/POR-Rasmussen survey conducted Oct. 9 found O'Donnell trailing the Democratic nominee by 16 points.

Following her upset victory over Rep. Mike Castle in September's GOP primary contest, O'Donnell became an overnight celebrity. But she has been widely mocked after clips from her guest appearances on comedian Bill Maher's talk show in the 1990s recently resurfaced. They feature the future Republican senatorial nominee talking about dabbling in witchcraft, calling evolution a "myth," and making other off-kilter comments.

When Coons was asked if he believes teachers' unions to be too powerful, he spoke for several minutes in an answer that consisted of 359 words but lacked a simple "yes" or "no." This prompted O'Donnell to snap: "If you notice, he didn't answer the question as to whether or not he thought the teacher unions were too powerful, and that's probably because he got their endorsement."

However, O'Donnell stumbled when moderators pressed her to name a recent Supreme Court ruling with which she disagreed, and she could not do so. "I'm very sorry," she apologized. "Right off the top of my head, I know that there are a lot, but I'll put it up on my website, I promise you." Immediately afterward, Coons, asked the same question, cited a case that had already come up in the evening's dialogue: Citizens United v. Federal Election Commission, the 2010 ruling that expanded corporations' ability to spend money in federal elections.

O'Donnell told Fox News afterward that she wasn't "caught off guard." She said that under former Chief Justice William Rehnquist and sitting Chief Justice John Roberts, "we've had some good decisions handed down."

"There haven't been a lot of recent decisions under this current court, and then Rehnquist before that, that, frankly, I disagree with. And that proves what happens when you get a good constitutionalist up there," she said.

But she said she believed she had succeeded in drawing a "line in the sand" between herself and Coons on the issues. "I hope that what we've done has served to shatter my opponent's glass jaw," she said.

O'Donnell was sometimes at a loss for words and other times flat-out unwilling to entertain the question during the debate. "What I believe is irrelevant," she begged off, when Blitzer asked if she still believes evolution to be a myth. She went on to explain that as a U.S. senator, she would vote to ensure that local school districts, not federal lawmakers, decide whether to teach "creationism" alongside, or in lieu of, the theory of evolution.

By contrast, Coons was sober and fluent, unfailingly correct in his grammar and supremely at ease in his command of facts, figures, issues, and policy. "The C-17 program, for example, or the second engine for the F-35," he offered without skipping a beat, when asked which programs he would cut to trim the deficit. Several times he prefaced his answers with sighing laments that time would not permit him to rebut all the false things O'Donnell had purportedly said.

Coons gave no clear answer when he was asked whether he supports the extension of the Bush-era tax cuts for those families earning more than $250,000 a year.

"I suppose extending the Bush tax cuts for the overwhelming majority of Americans," he said, before adding: "I don't think we should draw an arbitrary line at $250,000."

So where should the line be drawn?

"I think we should do those tax cuts that have the best chance of getting our economy going again," Coons offered, vaguely. Coons press aide Daniel McElhatton later told reporters his candidate is "not yet ready to commit" on the question.

Jason Mycoff, a professor of political science at the University of Delaware, expressed surprise at the negativity that permeated the 90-minute exchange.

"Both candidates showed a willingness to go after each other, pretty equally from both sides," Mycoff told reporters afterward. He thought Coons offered "wider, deeper responses on specific issues" and that O'Donnell "showed some of her political inexperience," particularly when she failed to answer the Supreme Court question.

However Mycoff also thought Coons was "obfuscating" in his lengthy, indeterminate response to the question about the Bush-era tax cuts. "I do not think the needle is going to move in terms of the polls," Mycoff predicted.

The two candidates are scheduled to participate in several more debates, including another on Thursday, before a local Rotary Club in Wilmington.

Fox News' James Rosen contributed to this report.