The president sealed his victory in Ohio, Iowa, New Hampshire and Colorado, four of the battleground states where the two rivals and their allies spent nearly $1 billion on dueling television commercials.

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WASHINGTON — President Obama on Tuesday won a second term in the White House, defeating Republican challenger Mitt Romney in a hard-fought election that served as a referendum on who could better ease Americans’ economic pain and uncertainty.

Obama spoke to thousands of cheering supporters in his hometown of Chicago, praising Romney and declaring his optimism for the next four years.

“While our road has been hard, though our journey has been long, we have picked ourselves up, we have fought our way back and we know in our hearts that for the United States of America, the best is yet to come,” he said.

He also vowed that “with your stories and your struggles, I return to the White House more determined and more inspired than ever about the work there is to do.”

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Romney made a graceful concession speech before a disappointed crowd in Boston. He asked all Americans to pray for Obama and urged the night’s political winners to put partisan bickering aside and “reach across the aisle” to tackle the nation’s problems.

Romney had earlier telephoned the president to concede.

Obama marched across the nation, scoring victory after victory in battleground states where the economy had mounted just enough of a comeback to persuade voters to give him four more years.

In first-day returns, Obama had 50 percent of the vote to Romney’s 49 percent.

The president’s laserlike focus on the battleground states allowed him to run up a 303-206 showing in the competition for electoral votes, where the White House is won or lost. It took 270 to win.

He held onto the coalition that led him to victory in 2008: women, Latinos, African Americans and young people. Romney, 65, seeking to become the first Mormon to win the presidency, was able to win only two states Obama had won last time, Indiana and North Carolina.

The second Democrat to win a second term since World War II, Obama, 51, swept the Northeast and West Coast states and won most of the Rust Belt battlegrounds, including Ohio, Michigan, Wisconsin and Pennsylvania. Romney won largely dependably Republican states across the South and into Texas and the Great Plains.

Romney conceded before a subdued crowd in Boston. “This is a time of great challenges for America, and I pray that the president will be successful in guiding our nation,” he said in a short speech.

Obama then took the stage in Chicago, entering as the song “Signed, Sealed, Delivered” played and a huge crowd cheered. “Tonight, more than 200 years after a former colony won the right to determine its own destiny, the task of perfecting our union moves forward,” the president said. “It moves forward because of you.”

Obama took office in January 2009 with a mandate to revive an economy struggling to recover from the Great Recession of 2007-2009, the worst downturn since the Great Depression. Six of 10 voters Tuesday said the economy was the most important issue, well ahead of health care or foreign policy. Three of four voters said the economy remained poor or not so good.

Obama touted the economy’s steady progress on his watch; Romney cited high unemployment and mounting federal debt as he argued the recovery’s pace was too slow. In the exit polls, slightly more than half said Obama was more in touch with people like them, compared with 44 percent for Romney.

Turnout was reported heavy, particularly in swing states as well as storm-battered New York and New Jersey. Experts still expected it to remain below 2008 levels, finding voters less engaged. About 32 million people had voted early, either in person or by mail.

The president spent Election Day in Chicago. He stopped by his campaign’s Hyde Park field office in south Chicago to greet workers and call voters. He called six Wisconsin voters, then talked to supporters at the office.

Romney voted in Belmont, Mass., and then made hastily scheduled campaign swings to Ohio and Pennsylvania. Ohio was considered crucial for Romney; no Republican has been elected president without winning the Buckeye State.

The last day’s scramble was vividly on display at the Cleveland airport. As Romney was waiting for his running mate, Rep. Paul Ryan of Wisconsin, to arrive, Vice President Joe Biden’s plane took off. Biden made his own last-minute visit to Ohio.

Romney visited a Cleveland-area campaign office, where he proclaimed, “This is a big day for change.”

And Obama was vulnerable. Within weeks of taking office in January 2009, he pushed through an $831 billion stimulus plan aimed at easing the recession’s impact. In 2010, he won approval of a historic overhaul of the nation’s health-care system, which will require nearly everyone to obtain coverage by 2014.

Both measures were passed with virtually no Republican support, and often bitter partisan wrangling. Republicans saw a huge political opening, and fueled by the tea-party movement, the party won control of the House in 2010 by protesting what it called Obama’s overreliance on and expansion of government.

At the same time, the economy struggled. The nation’s unemployment rate, 7.8 percent the month Obama took office, went to 10 percent that October and was 7.9 percent last month, more ammunition for the Republicans.

Obama, though, got some breaks. The economy recovered, slowly. Unemployment has dropped from its highs. Consumer confidence inched up. And Romney struggled at first to win the hearts of the conservatives who drive the Republican Party.

Obama exploited Romney’s past, recalling his support of Massachusetts’ abortion-rights laws and his support for the state’s health-care law, considered a model for the federal program.

Material from The Associated Press is included in this report.

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