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

“This happened because of you. Thank you,” Obama tweeted to supporters as he celebrated four more years in the White House.

After the costliest — and arguably the nastiest — campaign in history, divided government seemed alive and well.

Democrats retained control of the Senate with surprising ease. Republicans were on course for the same in the House, making it likely that Speaker John Boehner of Ohio, Obama’s partner in unsuccessful deficit talks, would reclaim his seat at the bargaining table.

Romney led narrowly in the popular vote, by about 30,00 votes out of more than 98 million cast, with ballots counted in 74 percent of the nation’s precincts.

But Obama’s laserlike focus on the battleground states allowed him to run up a sizeable margin in the competition for electoral votes, where it mattered.

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

Romney was in Massachusetts, his long and grueling bid for the presidency at an unsuccessful end.

He won North Carolina among the battleground states. Florida 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.

The economy was rated the top issue by about 60 percent of voters surveyed as they left their polling places. But more said former President George W. Bush bore responsibility for current circumstances than Obama did after nearly four years in office.

That bode well for the president, who had worked to turn the election into a choice between his proposals and Romney’s, rather than the simple referendum on the economy during his time in the White House.

Unemployment stood at 7.9 percent on election day, higher than when he took office. And despite signs of progress, the economy is still struggling after the worst recession in history.

There was no doubt about what drove voters to one candidate or the other.

About four in 10 said the economy is on the mend, but more than that said it was stagnant or getting worse more than four years after the near-collapse of 2008. The survey was conducted for The Associated Press and a group of television networks.

Polls were still open in much of the country as the two rivals began claiming the spoils of a brawl of an election in a year in which the struggling economy put a crimp in the middle class dreams of millions.

The president was in Chicago as he awaited the voters’ verdict on his four years in office. He told reporters he had a concession speech as well as victory remarks prepared. He congratulated Romney on a spirited campaign.

“I know his supporters are just as engaged, just as enthusiastic and working just as hard today” as Obama’s own, he added.

Romney reciprocated, congratulating the man who he had campaigned against for more than a year.

Earlier, he raced to Ohio and Pennsylvania for Election Day campaigning and projected confidence as he flew home to Massachusetts.

“We fought to the very end, and I think that’s why we’ll be successful,” he said, adding that he had finished writing a speech anticipating victory but nothing if the election went to his rival.

But the mood soured among the Republican high command as the votes came in and Obama ground out a lead in critical states.

Like Obama, Vice President Joe Biden was in Chicago as he waited to find out if he was in line for a second term. Republican running mate Paul Ryan was with Romney in Boston, although he kept one eye on his re-election campaign for a House seat in Wisconsin, just in case.

The long campaign’s cost soared into the billions, much of it spent on negative ads, some harshly so.

In the presidential race, an estimated one million commercials aired in nine battleground states where the rival camps agreed the election was most likely to be settled.

In a months-long ad war that cost nearly $1 billion, Romney and Republican groups spent more than $550 million and Obama and his allies $381 million, according to organizations that track advertising.

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