By Tom Cohen, CNN
(CNN) -- President Barack Obama and Republican challenger Mitt Romney described differing tax and economic plans at their first presidential debate on Wednesday night, arguing the other's proposals won't work in a continuation of major themes from their campaigns.
In exchanges full of policy proposals, facts and figures, Romney was more aggressive in the 90-minute encounter in criticizing Obama's record and depicting the president's vision as one of big government while Obama firmly defended his record and challenged his rival's prescriptions as unworkable.
"America does best when the middle class does best," Obama said in response to a question on job creation, adding that 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, however, said Obama still pushed the same policies as when he took office four years earlier, and those steps had failed to bring down high unemployment and get the economy surging again.
"It's going to take a different path," Romney said, repeating his five-point plan for growth that has been part of his stump speech
He rejected Obama's characterization of his tax plan, saying it won't add to the deficit, and criticized the president's call for allowing 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 750,000 jobs. I don't want to cost jobs," Romney said.
Obama responded that the revenue issue is "a major difference" he has with Romney, noting the former Massachusetts governor rejected the idea of cutting $10 in spending for every $1 in new revenue during the Republican primary campaign.
The candidates later clashed over major reform bills passed in Obama's first term, with Romney repeating his past pledge to repeal and replace the health care reform act and the Wall Street reform bill.
Insisting that regulation was necessary to keep the economy functioning, Romney said the Dodd-Frank Act passed in response to the financial crisis of 2008 was in some cases excessive.
He also repeated past criticism that the Affordable Care Act passed with no Republican support amounted to an unnecessary and unwanted government takeover of health care.
"The right answer is not to have the federal government take over health care," Romney said, adding 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.
Obama, however, said Romney has yet to provide full details of proposals to replace the Wall Street and health care reforms he has vowed to repeal.
"At some point, the American people have to ask themselves if the reason that Governor Romney is keeping all these plan secret is because they're too good," Obama said.
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.
The candidates sought to take advantage of what is expected to be their largest nationwide audience to date, making arguments for why voters should support them or reject the other guy.
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.
Both candidates had their wives in the audience at the University of Denver in Colorado for the debate taking place on the 20th wedding anniversary of the president and first lady Michelle Obama.
Obama opened the debate by promising his wife they wouldn't be celebrating their anniversary next year in front of 40 million people, and Romney joked that Obama found the most romantic place possible for the anniversary.
Analysts say Obama needed a presidential performance rather than fireworks or haymakers in order to maintain and build on a narrow edge in polls that indicate a very close election on November 6.
Romney, who has been unable to catch the president in most of the polls to date, sought to generate enthusiasm for a change in the White House as the nation wrestles with high unemployment, sluggish economic growth and mounting federal deficits and debt.
Romney has more recent debate experience -- he took part in 22 during the grueling GOP primary campaign of 2011-2012 that he ended up winning handily after fending off a litany of conservative contenders.
By contrast, Obama has not faced a debate since the three in 2008 with Sen. John McCain of Arizona, then the Republican presidential contender.
Wednesday's debate focused on the issue considered by voters to be the most crucial of the election -- the economy.
Romney "has to paint a compelling picture of a better economic future and why he can lead us there and President Obama can't," said GOP pollster Whit Ayres. Democratic pollster Peter Hart made a similar point, saying "if Romney loses this issue, then he is toast."
Jim Lehrer of PBS moderated his 12th presidential debate. He previously announced that the 90-minute event would include three segments on the economy and one each on health care, the role of government, and governing leadership and style. Each segment was scheduled for 15 minutes.
The two candidates shook hands and shared a laugh after being introduced by Lehrer as the audience applauded before being asked to remain silent for the remainder of the debate.
Organizers hoped the segmented format, with candidates given two minutes to answer questions, would allow for a more free-wheeling discussion instead of a series of rehearsed sound bites.
The other presidential debates will occur on October 16 in New York and October 22 in Florida. Vice President Joe Biden and Rep. Paul Ryan of Wisconsin, Romney's running mate, will debate on October 11 in Kentucky.
CNN's John King and Amy Roberts contributed to this report.