Mr Obama appeared in Wisconsin, accompanied by Bruce Springsteen, before going on to Iowa and Ohio.
The election will be decided by a handful of swing states, with Ohio in particular seen as crucial to victory.
Mr Obama and Mr Romney are running almost neck-and-neck in national polls, in a campaign that has cost more than $2bn (£1.2bn).
But surveys of the nine-or-so battleground states that will determine the election show Mr Obama narrowly ahead.
Legal challenges
The race has been most intense in Ohio - no Republican has ever made it to the White House without winning there.
Mr Romney would become the first Mormon president of the US if he wins on Tuesday.In Fairfax, Virginia just outside Washington DC, the former Massachusetts governor said the president had failed to make good on the promise of his 2008 campaign and it was time for a new direction.
"Look at the record," he exhorted supporters.
"Talk is cheap, but a record is real and it's earned with effort. When the president promised change, you can look and see what happened. Four years ago then-candidate Obama promised to do so very much but he's done so very little."
He summed up his pitch to voters: "Do you want four more years like the last four years? Or do you want real change?"
He was due to end his campaign with a late-night rally in New Hampshire but made the surprise announcement that he would extend campaigning into election day itself - visiting Ohio and Pennsylvania on Tuesday.
In Wisconsin, singer Springsteen helped warm up the Madison crowd for Mr Obama before the president appeared.
Mr Obama told the rally: "You may be frustrated with the pace of change. I promise you, so am I sometimes. But you know that I say what I mean and I mean what I say.
"I said I'd end the war in Iraq, and I ended it. I said I'd pass health care reform - I passed it. I said I'd repeal 'don't ask, don't tell' - we repealed it. I said we'd crack down on reckless practices on Wall Street, and we did.
"So you know where I stand, you know what I believe, you know I tell the
truth - and you know I'll fight for you and your families every single
day as hard as I know how, you know that about me."
With the election expected to be decided by a razor-thin margin, both sides are readying teams of lawyers for legal fights.
Democrats in Florida have filed a legal case demanding an extension of time available for early voting, citing unprecedented demand after voters reportedly queued up for hours on Sunday,
In Ohio, Republican election officials will go to court on Monday to defend an 11th-hour directive to local election officials that tightens requirements needed for provisional ballots to be counted.
A final poll published on Sunday by Ohio's Columbus Dispatch newspaper gave Mr Obama a 2% lead - 50% to 48% - over his rival, within the margin of error.
Activists have been stepping up efforts across the crucial swing states.
In Wisconsin, student volunteers have been putting in 14-hour
days in an effort to deliver the state for Mr Obama, the BBC's Paul
Adams reports from Madison.An opinion poll on Sunday for ABC News and the Washington Post put the two candidates at 48%, with even voters who term themselves independents split evenly on 46%.
Mr Romney remains favoured among whites, seniors and evangelical Christians; Mr Obama among women, non-whites and young adults.
The election is decided by the electoral college.
Each state is given a number of electoral votes in rough proportion to
its population. The candidate who wins 270 electoral votes becomes
president.A handful of governors, the entire House of Representatives and one-third of the Senate are also up for election on Tuesday.
Republicans are expected to keep control of the House, while Democrats were tipped to do the same in the Senate.
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