"Four years ago we were going through a major crisis," he said. "And yet my faith and confidence in the American future is undiminished."
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But Mitt Romney chose to look forward, and spoke of an America where Obamacare is repealed and the country's commitment to defense spending is renewed.
"You're going to continue to see a middle-class squeeze" if Obama is re-elected, Romney said.
The final statements were emblematic of the debate, in which Romney spend much of the night on the attack, while Obama was sometimes reticent and at times defensive.
The former Massachusetts governor, who seemed loose and comfortable, accused Obama of killing jobs, taxing the middle class and forcing his health care plan on America. Obama focused on policy and his efforts to dig the country out of the fiscal crisis of 2008.
On the economy, Romney again went on the offensive, accusing Obama of eliminating jobs by attempting to tax the country out of a recession -- a strategy he said can only fail.
"When the economy is growing slow like this, when we're in a recession, you shouldn't raise taxes on anyone," Romney said. "You raise taxes, and you kill jobs."
Obama defended his efforts to repair the economy, and characterized Romney's impression of small businesses as flawed. Romney believes the Donald Trumps of the business world qualify as small businesses, the president said.
The candidates also disagreed about Romney's tax-cut plan, which Obama described as a "$5 trillion tax cut" that would largely benefit the wealthy. Romney said his tax cuts would be nowhere near as dramatic, and repeatedly said that he would not lower taxes on high earners.
The debate began with a spirited exchange about whether Obama has done enough to repair the economy since he took office. Obama spoke to the camera and to moderator Jim Lehrer, while Romney often looked toward Obama, almost seeming to lecture him on economic policy.
"You've been president for four years. You said you'd cut the deficit. . . . We have a trillion-dollar deficit," Romney said, adding that economic growth, was at a standstill.
Obama said the resurgence of the U.S. auto industry and the recovery of the housing market are two indicators that he has stabilized the economy. The president was also quick to agree with Romney on two of his opponent's points -- that corporate taxes are too high and that America needs to boost its domestic energy production.
"We've begun to fight our way back," Obama said, who pointed out that he faced massive economic problems "when I walked into the Oval Office."
Obama said Romney's tax-cut plan would harm middle-income Americans.
Romney accused Obama of mischaracterizing his tax cut plan, which he said would buoy the middle class during the soft economy. He also said he would push for energy independence, open up trade with Latin America and "champion small business." Romney painted the president as an enemy of Main Street.
"New business start-ups are down to a 30-year low," Romney said, adding that Obama believes "a bigger government, taxing more, spending more."
The partisan gridlock that rules Washington won't end under a President Mitt Romney because of Romney's inability to push back against his own party's far right wing, Obama said.
Romney "has not displayed a willingness to say 'No' to some of the more extreme" factions of the Republican party, Obama said, adding that sometimes leadership means "saying no."
But Romney said ending partisanship in Washington is not about party but about leading by example.
"We need leadership," Romney said, adding that November's election is about "the course for America."
The candidates also traded barbs on education. Obama described Romney as being out of touch with working families because of his belief that a student "should borrow money from your parents to go to college." Romney said his commitment is not to cut education funding but to make it "more efficient and more effective."
The two went back and forth on health care, with Obama trumpeting Obamacare as a success and Romney chiding it as a job killer.
Obama pointed to similarities between his health care plan and the plan approved in Massachusetts when Romney was governor, describing them as "the same plan."
"We now have a system where we have the opportunity to start bringing down costs," Obama said.
Romney said the Massachusetts plan is modeled for the state level, which he said is where health care reform should take place. The federal plan has raised taxes by $1 trillion, he said.
"What we did in Massachusetts is a model for the nation -- state by state," Romney said, adding that forcing the plan through on the federal level is "not the course for America."
Obama also used the debate to paint Romney as an enemy of Medicare. But Romney struck back that the president is funneling money out of the program -- a critical issue for millions of senior citizens.
Romney attacked Obama about Medicare, which Romney said the president has cut by $716 billion. Obama disputed Romney's charge, and faulted Romney for supporting the adoption of a voucher system for seniors in the future.
"What I propose is no change" to present-day Medicare, Romney said, adding that future seniors should be allowed to choose between Medicare and a private plan.
Obama said Medicare is more fiscally solvent than private insurers and that voucher plans will put seniors at risk, and put them "at the mercy of those insurance companies."
The University of Denver debate -- the first of three for the candidates -- was divided into six segments of 15 minutes. The candidates get two minutes to answer an opening question, with the rest of the debate controlled by the moderator.
It focused on the economy, health care and other domestic issues, with Lehrer of PBS serving as moderator. Obama received the first question and Romney delivered the final answer.
Romney had a private tour of the debate hall Wednesday afternoon, The Associated Press reported. Obama planned a walk-through after arriving from Nevada, where he spent three days in practice sessions. Romney's aides said he reviewed briefing books and policy at a Denver hotel.
Five weeks before Election Day, early voting is under way in scattered states and will be starting in more states every day. Opinion polls show Obama with an advantage nationally and in most if not all of the battleground states where the race is most likely to be decided.
A Quinnipiac University poll that focused on the final week of September had Obama leading 49 percent to 45 percent for Romney, with four percent undecided or declining to answer and the remaining two percent favoring another candidate.
The state of the polls put pressure on Romney to come up with a showing strong enough to alter the course of the campaign, political observers said.
"We cannot afford four more years like the last four years," Ed Gillespie, a senior adviser to The Romney campaign, told the Washington Post. "Whether it's health care, energy, taxes and spending and debt, foreign policy, the message is we cannot afford four more years like the last four years."
Robert Gibbs, a senior adviser to the Obama campaign, has in turn also criticized the Romney campaign for not offering more specifics on their tax plan while defending the president's budget.
"If you look at the budget plan that the president has outlined, he has a $4 trillion spending cut plan making sure that our tax code is fair and that those on the upper end of that tax code are paying more," Gibbs told CBS News.
The sputtering economy is expected to serve as the debate backdrop, as it has for virtually everything else in the 2012 campaign for the White House. Obama took office in the shadow of an economic crisis and economic growth has been sluggish throughout his term, with unemployment above 8 percent since before he took office.
Both campaigns engaged in a vigorous pre-debate competition to set expectations, each side suggesting the other had built-in advantages.
Romney took part in 19 debates during the campaign for the Republican primary early in the year, The Associated Press reported. The president has not been onstage with a political opponent since his last face-to-face encounter with Arizona Sen. John McCain, his Republican rival in 2008.
Obama and Romney prepared for the evening with lengthy practice sessions, The Associated Press reported. Romney selected Ohio Sen. Rob Portman as a stand-in for the president; Obama turned to Massachusetts Sen. John Kerry to play the Republican role.
Buzz about the Denver debate turned Colorado into perhaps this year's top battle ground state, Politico reported. The Denver area ranked as the top battleground state ad market from Sept. 9 through Sept. 30, the website reported.
A Wesleyan Media Project analysis of media data reported that Denver-area voters saw 7,770 ads in that time period, with 4,791 from the Obama campaign and Democratic groups, and 2,979 from the Romney campaign, the RNC and Republican groups. Las Vegas was second, with 7,360 spots, and Cleveland third at 6,583. The top 15 markets ranked by ads encompassed five states -- Colorado, Florida, Nevada, Ohio and Virginia, Politico reported.
"It's worth noting that the time period covered by the study largely coincides with Obama's surge in the polls, suggesting the ad disparity played a role in amplifying the convention bounce in a handful of key swing states," wrote Politico's Charles Mahtesian in an article on the website.
Eyes will shift to New York, and Long Island, later this month, when the presidential rivals arrive here for their second debate.
Obama and Romney are scheduled to debate on Oct. 16 at Hofstra University in Uniondale and Oct. 22 in Boca Raton, Fla. Vice President Joe Biden and Republican Rep. Paul Ryan of Wisconsin have one debate, Oct. 11 in Danville, Ky.
Newsday has reported that tickets to the debate are not available to the public -- they are instead being distributed to the two campaigns, the school and debate sponsors to hand out as they please, according to the Commission on Presidential Debates, the nonpartisan group that's been running the debates since 1988.
"Everyone in New York is eagerly anticipating this debate," Michael Waller, executive director of the New York Republican Party, has said. "It not only focuses attention on our state . . . but it also shines a spotlight on some of our down-ticket races."
With The Associated Press