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The general consensus is that the biggest prize on the board is the one state that both men visited Sunday: Ohio, where the latest Real Clear Politics average of polls showed Mr. Obama with a 3-point lead.

No Republican has won the White House without winning the Buckeye State — though, by most counts, there are two alternative ways for Mr. Romney to win the 270 electoral votes needed to sew up the election. In short, he would need to combine wins in North Carolina, Colorado, Florida and Virginia with either a surprise victory in Pennsylvania or a win in Wisconsin coupled with a victory in either Iowa or New Hampshire.

With little room for error, the Romney camp announced Monday that after Mr. Romney and his wife, Ann, cast their ballots Tuesday morning in Belmont, Mass., Mr. Romney will hold last-minute campaign events in Cleveland and Pittsburgh.

A referendum on Obama

Mr. Obama, a 51-year-old former college law professor and community organizer and senator, became the first black man elected president four years ago, sweeping into office on a message of “hope and change” that made him a worldwide phenomenon.

But after inheriting a recession from President George W. Bush, Mr. Obama was dogged by an unemployment rate that stayed above 8 percent for more than 40 straight months, and the soaring national debt, which moved past $16 trillion during his term.

That left him vulnerable to attacks from Mr. Romney, who applauded Mr. Obama for approving the Navy SEAL raid that resulted in the killing of terrorist Osama bin Laden, but otherwise argues that the policies the president has embraced — in particular, Obamacare — have slowed the nation’s economic recovery.

Back on the campaign trail Monday, Mr. Obama defended his record, saying the “status quo” in Washington has spent millions of dollars over the course of his first term trying to block the president’s attempts to reform the health care system and crack down on Wall Street shenanigans.

“What they’re counting on now is that you’re going to be so worn down, so fed up, so tired of all the squabbling, so tired of all the dysfunction that you’re just going to give up and walk away and leave them right where they are — pulling the strings, pulling the levers — and you locked out of the decisions that impact your lives,” Mr. Obama said. “In other words, they’re betting on cynicism. But, Wisconsin, my bet’s on you. My bet’s on you.”

Romney’s bid for history

Meanwhile, Mr. Romney, a 65-year-old former venture capitalist and Massachusetts governor, is taking a second stab at becoming the first Mormon to win the presidency.

Mr. Romney spent a good chunk of the bruising GOP primary assuring the party’s conservative base that he was one of them: fending off the criticism aimed at the universal health care law he signed in Massachusetts and his evolution from being pro-choice to pro-life. He also staked out the toughest line against illegal immigration and told voters he was “severely conservative.”

Mr. Romney has since moderated his message and injected momentum into his flagging campaign with a series of well-received debate performances.

In the waning days of the campaign, Mr. Romney played up the notion that his gubernatorial record in Massachusetts shows that he is the kind of postpartisan figure who can end the brinkmanship in Washington that threatens to push the nation into a double-dip recession.

“That’s why I’m running for president,” Mr. Romney said Monday during the stop in Lynchburg, Va., a conservative stronghold. “I know how to change the nation, how to get it back on course, how to create jobs, how to get a balanced budget, how to get rising take-home pay. Accomplishing real change is not something I just talk about. It’s something I’ve done, and it’s what I’m going to do when I’m president of the United States of America.”