HOLLYWOOD, Fla. — Two days from judgment by the voters, President Barack Obama raced through four far-flung battleground states on Sunday while Mitt Romney ventured into traditionally Democratic Pennsylvania, seeking a breakthrough in a close race he mused aloud he might lose.

Appearing before some of the largest crowds of the campaign, the two rivals stressed their differences on the economy, health care and more while professing an eagerness to work across party lines and end gridlock in Washington.

“You have the power,” Obama, the most powerful political leader in the world, told thousands of cheering supporters in New Hampshire, his first appearance of a day not scheduled to end until after midnight in the East.

Later, in Cleveland, boos from Romney’s partisans turned to appreciative laughter when the Republican nominee began a sentence by saying, “If the president were to be elected,” and ended it with, “It’s possible but not likely.” It was a rare public acknowledgement that despite expressions of confidence from him and his aides, defeat was a possibility.

In a campaign that began more than a year ago, late public opinion polls were unpredictably tight for the nationwide popular vote. But they suggested at least a slim advantage for the president in the state-by-state competition for electoral votes that will settle the contest, including Ohio, Wisconsin, Iowa and Nevada.

Conceding nothing, Romney flew to Pennsylvania for his first campaign foray of the general election. The state last voted for a Republican presidential candidate in 1988, and Obama’s aides insisted it was safe for the president. Yet the challenger and his allies began advertising heavily in the campaign’s final days, and public and private polls suggested the state was relatively close.

The theme from “Rocky” blared from the loudspeakers as he stepped to the podium. “The people of America understand we’re taking back the White House because we’re going to win Pennsylvania,” Romney told a large crowd that had been waiting for hours on a cold night.

Earlier, Romney launched a new television commercial, possibly his last of the campaign, as he appeared in Iowa, Ohio and Virginia as well as Pennsylvania. “He’s offering excuses. I’ve got a plan” to fix the economy. “I can’t wait for us to get started,” he said.

In Des Moines, Romney said he would meet regularly with “good men and women on both sides of the aisle” in Congress. Later, in Cleveland, he said of Obama, “Instead of bridging the divide, he’s made it wider.”

Obama had New Hampshire, Florida, Ohio and Colorado in his sights for the day, and, judging from the polls, a slight wind at his back. So much so that one conservative group cited a string of surveys that favor the president as it emailed an urgent plea for late-campaign donations so it could end his time in the White House.

In Florida, the president said he wants to work across party lines, but quickly added there were limits to the sorts of compromises he would make.

“If the price of peace in Washington is cutting deals that will kick students off of financial aid, or get rid of funding for Planned Parenthood, or let insurance companies discriminate against people with preexisting conditions, or eliminate health care for millions who are on Medicaid .... I’m not willing to pay that price,” he said, reciting some of the charges he has leveled against Romney.

The two rivals and their running mates flew from state to state as the last of an estimated 1 million campaign commercials were airing in a costly attempt to influence a diminishing pool of voters.

Obama, his voice growing hoarse after four straight days of heavy campaigning, spoke briefly to an overflow crowd of 2,000 at a Cincinnati basketball arena Sunday night. The president projected confidence in his off-the-cuff remarks, telling backers he would need their support “even after the election.”

“I intend to win Ohio. I intend to win the presidency,” he said. “But even after that I’m going to need all of you involved to make sure we don’t let up.”

More than 27 million ballots have been cast in 34 states and the District of Columbia, although none will be counted until Election Day on Tuesday.

Nearly 4 million of them were deposited by Floridians, and Democrats cited unprecedented demand for pre-election day voting as they filed a lawsuit demanding an extension of available time. A judge granted their request in one county where an early voting site was shut down for several hours on Saturday in a bomb scare.

Obama and Romney disagree sharply about the approach the nation should take to the slow-growth economy and high unemployment, and the differences have helped define the campaign.  Most notably, Romney wants to extend tax cuts that are due to expire without exception, while Obama wants to allow them to lapse on incomes over $250,000.

At the same time, polls show bipartisanship is popular, in the abstract, at least, which accounts for the emphasis the candidates are placing in the race’s final days on working across political aisles.

Romney frequently cites his ability to work with the Democratic-controlled Legislature while he was governor of Massachusetts, although he rarely mentions the veto battles he had.

Obama’s term has been littered with the legislative wreckage left behind by constant struggles with congressional Republicans. Yet his trip to New Jersey last Wednesday was a model of nonpartisanship as he accompanied Republican Gov. Chris Christie on a tour of destruction caused by Superstorm Sandy. The governor repeatedly praised the administration’s response to the storm.

One prominent Republican said the storm had worked to Romney’s disadvantage in a different way.

“The hurricane is what broke Romney’s momentum. I don’t think there’s any question about it,” former Mississippi Gov. Haley Barbour said on CNN’s “State of the Union.”

“Any day that the news media is not talking about jobs and the economy, taxes and spending, deficit and debt, Obamacare and energy, is a good day for Barack Obama,” he said. “Now, whether it will be good enough remains to be seen.”

Romney’s campaign wanted no part of that.  “I don’t look at what happened with the storm and how it affected so many people through a political lens,” said a spokesman, Kevin Madden.

So intense was the campaigning that Vice President Joe Biden’s plane and the one carrying Romney were both on the tarmac in Cleveland at the same time in early afternoon. The two men did not see one another.

Biden’s assignment for the day was to rally voters across Ohio. “These guys are trying to play a con game here at the end,” he said of Romney and Ryan, whom he accused of posing as more moderate than they are.

Ryan started out in his home state of Wisconsin. He donned a Green Bay Packers jacket and a yellow and green striped tie for a pregame tailgating party he attended briefly across the street from fabled Lambeau Field.

Then, football or no football, it was off to Ohio, Minnesota and Colorado.