By Tom Cohen
(CNN) -- President Barack Obama and Mitt Romney return to the campaign trail in battleground states on Thursday after going toe-to-toe on dominant campaign issues of taxes, healthcare and the economy in a debate that analysts and a snap poll agreed the Republican challenger won.
In exchanges full of policy proposals, facts and figures, Romney was more aggressive in the 90-minute encounter on Wednesday night at the University of Denver, the first of three debates ahead of the November election.
A forceful Romney criticized Obama's record and depicted the president's vision as one of big government, while the Democratic incumbent defended his achievements and challenged his rival's prescriptions as unworkable.
The post-debate verdict swung clearly to Romney.
"A week ago, people were saying this was over. We've got a horse race," said CNN Senior Political Analyst David Gergen, who called the debate Romney's best so far after the 22 the former Massachusetts governor took part in during the GOP primary campaign.
Alex Castellanos, a Republican strategist and CNN contributor, expressed surprise at Romney's strong performance, saying he "rose to the moment" and seemed to benefit from the multiple primary debates.
"It looked like Romney wanted to be there and President Obama didn't want to be there," noted Democratic strategist and CNN contributor James Carville. "The president didn't bring his 'A' game."
The CNN/ORC International poll of 430 people who watched the debate showed 67% thought Romney won, compared to 25% for Obama.
Obama remains in Colorado for his first post-debate appearance before heading to Wisconsin. Romney joins running mate Rep. Paul Ryan at a rally in Virginia. Meanwhile, Vice President Joe Biden will speak at an Iowa campaign event.
The next presidential debate is October 16 in New York, and the third takes place on October 22 in Florida. Biden and Ryan will debate on October 11 in Kentucky.
On Wednesday, neither presidential candidate scored dramatic blows that will make future highlight reels, and neither veered from campaign themes and policies to date.
But Romney came off as the more energized candidate overall by repeatedly attacking Obama on red-meat issues for Republicans such as health care reform and higher taxes, while the president began with lengthy explanations and only later focused more on what his opponent was saying.
Moderator Jim Lehrer of PBS had trouble keeping the duo within time limits for responses, especially Obama, who ended up speaking four minutes longer than Romney.
Romney's strongest moments came in emphasizing his frequent criticism of Obama's record, saying the nation's high unemployment and sluggish economic recovery showed the president's policies haven't worked.
"There's no question in my mind if the president is re-elected, you'll continue to see a middle-class squeeze," Romney said, adding that another term for Obama also will mean the 2010 Affordable Care Act, known as Obamacare, "will be fully installed."
At another point, he noted how $90 billion spent on programs and policies to develop alternative energy sources could have been devoted to hiring teachers or other needs that would bring down unemployment.
Obama argued that his policies were working to bring America back from the financial and economic crisis he inherited, and that Romney refused to divulge specifics about his proposed tax plans and replacements for the health care law and Wall Street reform that the Republican has pledged to repeal.
"At some point, the American people have to ask themselves if the reason that Governor Romney is keeping all these plans secret is because they're too good," Obama said, adding the answer was "no" and that the lack of details reflected the difficulty in making touch decisions.
In particular, Obama said Romney's plan of tax cuts for the rich had failed before and would fail again now.
Describing the Romney tax plan as a $5 trillion cut, Obama echoed a line from former President Bill Clinton by saying the math doesn't add up without increasing tax revenue, which Romney rejects.
"I think math, common sense and our history shows us that's not a recipe for job growth," Obama said.
Romney rejected Obama's characterization of his tax plan, saying it won't add to the deficit, and he criticized the president's proposal to allow tax rates on income over $250,000 for families and $200,000 for individuals to return to the higher rates of the 1990s.
"The National Federation for Independent Businesses has said that will cost 700,000 jobs. I don't want to cost jobs," Romney said.
Obama responded that the revenue issue is "a major difference" he has with Romney over the overall question of deficit reduction, noting the former Massachusetts governor had rejected the idea of cutting $10 in spending for every $1 in new revenue during the Republican primary campaign.
In his strongest line of the night, Obama said Romney lacked the important leadership quality of being able to say "no" when necessary.
"I've got to tell you, Governor Romney, when it comes to his own party during the course of this campaign, has not displayed that willingness to say no to some of the more extreme parts of his party," Obama said in reference to his challenger's swing to the right during the primaries to appeal to the GOP's conservative base.
Romney repeatedly went after Obama on the health care reform bill, criticizing the president for focusing so strongly on a measure that passed with no Republican support instead of devoting more attention to creating jobs.
"I just don't know how the president could have come into office, facing 23 million people out of work, rising unemployment, an economic crisis at the -- at the kitchen table, and spend his energy and passion for two years fighting for Obamacare instead of fighting for jobs for the American people," Romney said.
"The right answer is not to have the federal government take over health care," Romney added, quickly noting his plan would include popular provisions of Obamacare such as allowing children up to age 26 stay on family plans and preventing insurers from denying coverage for pre-existing conditions.
In response, Obama said Romney's stance to have states craft their own health care plans would allow insurance companies to return to past practices that hurt consumers.
With polls narrowing less than five weeks before Election Day, Obama and Romney launched a new phase in a bitter race dominated so far by negative advertising as both camps try to frame the election to their advantage.
Whether it matters is itself a topic of debate. According to an analysis by Gallup, televised debates have affected the outcome of only two elections in the past half century -- Nixon-Kennedy in 1960 and Bush-Gore in 2000.
Lehrer, moderating his 12th presidential debate, planned to break up the debate into 15-minute segments focusing on different aspects of the economy and other domestic issues. However, the exchanges by the candidates scrambled the format, with the opening discussion on taxes lasting more than 20 minutes.
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