Vice President Joe Biden swiftly broadened the attack, accusing Republicans of seeking to undermine the decades-old federal program millions of seniors rely on for health care. "We are for Medicare. They are for voucher care," he said.
The president and vice president campaigned separately across three battleground states as delegates descended on the Democrats' convention city for two days of partying before their first official meeting Tuesday in the Time Warner Cable Arena.
An enormous sand sculpture made in Obama's likeness served as a reminder, as if any were needed, that the Democrats were in town.
Some 800 demonstrators marched through the streets around the convention hall, protesting what they call corporate greed as well as U.S. drone strikes overseas, said to kill children as well as terrorists. Dozens of police officers walked along with the protesters' parade, carrying gas masks, wooden batons and plastic hand ties. One arrest was reported, for public intoxication.
The economy is the dominant issue of the campaign, and Biden's itinerary, in particular, underscored the threat that a sluggish recovery and high, 8.3 percent unemployment pose to Democrats seeking another term in power. He was in Pennsylvania and Wisconsin, states that have received little attention previously as the candidates, their parties and outside allies concentrate on the areas of the country deemed most competitive. His presence suggested the race in both states was tightening.
There was additional evidence of the same concern, as the president's senior surrogates refused to give a direct answer when asked on Sunday morning television programs if Americans are better off than they were four years ago.
"We've clearly improved ... from the depths of the recession," said David Plouffe, one of Obama's top White House aides.
He sought to swiftly turn the question into criticism of the Republicans.
"The Romney path would be the wrong path for the middle class, the wrong path for this country," he insisted.
Asked the same better-or-not question that has become a staple of presidential campaigns, another top adviser, David Axelrod answered, "I think the average American recognizes that it took years to create the crisis that erupted in 2008 and peaked in January of 2009. And it's going to take some time to work through it."
Obama spoke on the University of Colorado campus in Boulder, and made his by-now familiar plea for students to register and vote. He benefited enormously from the support of younger voters four years ago and can ill-afford a fall-off in their support - or enthusiasm- in 2012.
Democrats regard passage of a sweeping health care law as a high point of achievement for Obama during his term. Yet the law has also unified Republicans who argue it amounts to a government takeover of the health care system and a budget-buster to boot.
Obama has lately been eager to answer his critics, and he did more than that in his speech.
"Gov. Romney promised that on his first day in office he's gonna sit right down, grab a pen and repeal Obamacare," the president said, referring to the law by the name Republicans first attached to it as an insult.
"What that means is that right away he'd kick 7 million young people off their parents' plan. He'd take hope away from tens of millions of American with pre-exiting conditions by repealing reform," the president said.
"You know, he calls it Obamacare. I like the name. I do care. .... I don't know exactly what the other side is proposing; I guess you could call it 'Romney doesn't care.' But this law is here to stay."
Romney has provided only a few details of his plans to replace the law he wants to wipe off the books. In particular, he says the requirement for coverage - also part of a state law he signed as governor of Massachusetts - should not apply nationally.
He proposes to guarantee that a person who is "continuously covered" for a certain period be protected against losing insurance if he gets sick, leaves his job and needs another policy.
Amanda Henneberg, a spokeswoman for the Romney campaign, said, "It is outrageous and offensive for President Obama to suggest that the majority of Americans who oppose Obamacare do not care about Americans suffering with serious, long-term medical conditions."
She said Romney believes his own plan would "replace Obamacare with patient-centered reforms, which include multiple elements to help those with pre-existing conditions, will better achieve the affordable access to high quality health care that the American people actually want."
As for Biden's remarks, the campaign also renewed its criticism of Obama for cutting projected Medicare spending by more than $700 billion as part of the health care law.
Romney spent Sunday at his Wolfeboro, N.H., vacation home, leaving only to attend church services with his wife, Ann.
Aides said he would spend much of the Democrats' convention week preparing for three fall debates with Obama, beginning on Oct. 3.
Running mate Paul Ryan was booked into North Carolina, counterprogramming the Democratic convention rhetoric.
Biden's appearance in Green Bay, Wis., was mostly devoted to domestic issues.
Earlier, campaigning in York, Pa., he took a swipe at Romney on foreign policy.
"He said it was a mistake to end the war in Iraq and bring all of our warriors home," the vice president said. "He said it was a mistake to set an end date for our warriors in Afghanistan and bring them home. He implies by the speech that he's ready to go to war in Syria and Iran. "
Democrats have been critical of Romney for making no mention of the war in Afghanistan when he accepted the Republican nomination in Tampa, Fla., last week. He previously criticized Obama for setting a public date for the withdrawal of U.S. combat troops from the war.
Romney also has faulted Obama for allowing the government of Syrian President Bashar Assad to remain in power. Yet his aides have refused to say for a week if he agrees with French President Hollande's promise to extend diplomatic recognition to a provisional government if Syrian rebels form one.
San Antonio Mayor Julian Castro delivers the keynote speech on Tuesday, followed by First lady Michelle Obama's remarks.
Obama and Biden will be nominated for second terms on Wednesday night, when former President Bill Clinton has the role of star speaker.
Biden and Obama, deliver their nomination acceptance speeches on Thursday, the convention's final night.
Ben Feller reported from Boulder, Colo. Associated Press writers Philip Elliott in York, Pa., Kasie Hunt in Wolfeboro, N.H., and Michael Biesecker, Mitch Weiss and Beth Fouhy in North Carolina contributed to this story.