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.
"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.