Not surprisingly, the two men disagreed over Medicare, a flash point since Romney placed Wisconsin Rep. Paul Ryan on his ticket.
The president repeatedly described Romney's plan as a “voucher program” that would raise out-of-pocket costs on seniors.
He continued, directly addressing the voters at home: “If you're 54 or 55 you might want to listen because this will affect you.”
Romney said he doesn't support any changes for current retirees or those close to retirement.
“If you're 60 or 60 and older you don't need to listen further,” he said, but he contended that fundamental changes are needed to prevent the system from becoming insolvent as millions of baby boom generation Americans become eligible.
Romney also made a detailed case for repealing Obamacare, the name attached to the health care plan that Obama pushed through Congress in 2010. “It has killed jobs,” he said, and argued that the best approach is to “do what we did in my state.”
Though he didn't say so, when he was governor Massachusetts passed legislation that required residents to purchase coverage — the so-called individual mandate that conservatives and he oppose on a national level.
Romney also said that Obamacare would cut $716 billion from Medicare over the next decade.
The president said the changes were part of a plan to lengthen the program's life, and he added that AARP, the seniors lobby, supports it.
Jim Lehrer of PBS drew moderator's duties, with Obama getting the first question and Romney the last word.
Five weeks before Election Day, early voting is under way in scattered states and beginning in more 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.
That put particular pressure on Romney to come up with a showing strong enough to alter the course of the campaign.
The sputtering economy served 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 but promised a turnaround that hasn't materialized. Economic growth has been sluggish throughout his term, with unemployment above 8 percent since before he took office.
The customary security blended with a festival-like atmosphere in the surrounding area on a warm and sunny day. The Lumineers performed for free, and Black Eyed Peas frontman will.i.am delivered a pep talk of sorts to Obama's supporters. School officials arranged to show the debate on monitors outside the hall for those without tickets.
There was local political theater, too, including female Romney supporters wearing short shorts and holding signs that said, “What War On Women?” — a rebuttal to claims by Obama and the Democrats.
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 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. 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.
The two presidential rivals also are scheduled to debate on Oct. 16 in Hempstead, N.Y., 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. Both men have already begun holding practice sessions.
Associated Press writer Kristen Wyatt contributed to this story. David Espo reported from Washington.