(CBS News)-- After months of heated, sometimes nasty, campaigning, President Obama and Mitt Romney met in the same room on the same stage for the first of three debates, this one focusing specifically on the top issue on voters' minds: the economy.
At the University of Denver, in the battleground state of Colorado, moderator Jim Lehrer threw the first question to President Obama, who was first up after winning a coin toss. Beyond the cordial, obligatory opening remarks, which included the president wishing his wife, Michelle, a happy 20th wedding anniversary, the debate quickly turned to the economy.
The opening remarks of the debate broadly defined the differing visions of the two candidates.
"Are we doing to double down on the top-down" economic plan that Romney proposes, the president said, criticizing Romney for an economic plan that benefits the wealthy, "or do we embrace a new economic patriotism?" Mr. Obama asked, which he defined as an economic approach of shared sacrifice and a focus on the middle-class.
Romney responded recounting a story of a young couple who is struggling and just lost their home. He said he "can help" such families, but it's "It's going to take a different path." He added, "The president has a view very similar to the view he had when he ran four years, that a bigger government, spending more, taxing more, regulating more -- if you will, trickle-down government -- would work."
Prior to the start of the debate, an Obama campaign aide said the president's aim is not to attack Romney but "will correct Romney's attacks as needed," adding that his "number one goal" is to lay out his plans for the next four years.
The president hit a common theme he often addresses on the campaign trail, slamming Romney's tax plan for cutting taxes by $5 trillion dollars without defining how he would pay for it.
"How we pay for that, reduce the deficit, and make the investments that we need to make, without dumping those costs onto middle-class Americans, I think is one of the central questions of this campaign," the president said.
Romney quickly refuted the president's argument. "Virtually everything he just said about my tax plan is inaccurate," Romney said. He said his plan would cut taxes for the middle class, but wouldn't reduce the "share" of taxes high-income earners pay.
"High-income people are doing just fine in this economy. They'll do fine whether you're president or I am," Romney said. "I will not reduce the taxes paid by high-income Americans."
Mr. Obama chided, "Well, for 18 months he's been running on this tax plan. And now, five weeks before the election, he's saying that his big, bold idea is, 'Never mind.'"
He also questioned Romney's mathematics ability, saying, "[T]he fact is that if you are lowering the rates the way you described, Governor, then it is not possible to come up with enough deductions and loopholes that only affect high-income individuals to avoid either raising the deficit or burdening the middle class. It's -- it's math. It's arithmetic."
Turning to the issue of Medicare, Romney said definitively, "What I support is not change for current retirees. And the president supports taking $716 billion out of that program."
Responding to Romney's insistence that his plan would not impact people currently on Medicare, the president turned to the camera and said, "If you're 54 or 55, you might want to listen because this might affect you."
The president described Romney's plan as a voucher system that would cause seniors to pay more.
Romney said his plan would offer seniors the choice of the government's Medicare program or insurance-run health coverage.He also said he would means-test Medicare benefits, which means high-income earners would receive lower benefits.
Both candidates and their campaigns spent the days leading up to the debate trying to lower expectations, downplaying their debate-skills and insisting that they didn't need to "win" the debate.
Tonight's debate skewed from its format of six 15-minute segments, but the debate still covered the broad issues of the economy, health care, the role of government, and governing. Each candidate received two minutes to respond to each topic followed by a Lehrer-moderated discussion.
In the debate section that focused on health care, the Affordable Care Act being the center of the discussion.
Romney said he would replace the health care law because it adds to the cost of health care, cuts $716 billion from Medicare and put in place "an unelected board" to make health care decisions.
"It's expensive and expensive things hurt families," Romney said.
"We've seen the model work really well in Massachusetts," the president shot back, referring to the universal health care plan Romney signed as governor of Massachusetts. "It hasn't destroyed jobs," he added.
"I like the way we did it in Massachusetts," Romney responded, insisting that each state should decide its health care plan. "What we did in Massachusetts is a model for he nation, state by state."
"Free enterprise is more effective of bringing down the cost," Romney said. "The right answer is not to have the federal government take over health care and start" issuing mandates.
In response to the president's criticism that Romney has yet to describe how he would replace the health care law, the governor said his plan is "lengthy." He described two components that are part of his plan that were recently implemented through the president's health care law, including allowing people with pre-existing conditions and allowing young people to stay on their parents' insurance.
While both candidates spent most of the past several days off the campaign trail preparing for tonight's debate, they have two more opportunities to meet.
Romney and Mr. Obama have two more opportunities to debate each other, on October 16 at Hofstra University in East Hempstead, N.Y., and on October 22 at Lynn University in Boca Raton, Fla. The vice presidential nominees, Vice President Joe Biden and GOP Rep. Paul Ryan, square off in their first and only debate next Thursday, October 11 at Centre College in Danville, Ky.