WASHINGTON — President Barack Obama rolled to re-election Tuesday night, vanquishing former Massachusetts Gov. Mitt Romney despite a weak economy that plagued his first term and put a crimp in the middle class dreams of millions. In victory, the president confidently promised better days ahead.

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.

Romney made his own graceful concession speech before a disappointed crowd in Boston. He summoned 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.

Still, after the costliest — and one of the nastiest — campaigns in history, divided government was alive and well.

Democrats retained control of the Senate with surprising ease.

Republicans did the same in the House, ensuring that Speaker John Boehner of Ohio, Obama’s partner in unsuccessful deficit talks, would reclaim his seat at the bargaining table.

At Obama headquarters in Chicago, a huge crowd gathered waving small American flags and cheering. Supporters hugged each other, danced and pumped their fists in the air. Excited crowds also gathered in New York’s Times Square, at Faneuil Hall in Boston and near the White House in Washington, drivers joyfully honking as they passed by.

With returns from 84 percent of the nation’s precincts, Obama had 53.7 million, 49.6 percent of the popular vote. Romney had 53 million, or 48.9 percent.

The president’s laserlike focus on the battleground states allowed him to run up a 303-206 margin in the competition for the 270 electoral votes needed to win the White House, the count that mattered most. Remarkably, given the sour economy, he lost only two states that he captured in 2008, Indiana and North Carolina.

Florida, another Obama state four years ago, remained too close to call.

The election emerged as a choice between two very different visions of government — whether it occupies a major, front-row place in American lives or is in the background as a less-obtrusive facilitator for private enterprise and entrepreneurship.

Obama captured Ohio, Wisconsin, Iowa, Virginia, New Hampshire, Colorado and Nevada, seven of the nine states where the rivals and their allies poured nearly $1 billion into dueling television commercials.