COLUMBUS, Ohio — President Barack Obama enters the final hours of the 2012 campaign with an edge in the hunt for the 270 electoral votes needed to win and more ways to reach that magic number. Yet the race is remarkably close in at least six states that could go either way, giving Republican Mitt Romney hope that he can pull off a come-from-behind victory.

If the election were held now, an Associated Press analysis found that Obama would be all but assured of 249 votes by carrying 20 states that are solidly Democratic or leaning his way — Iowa, Nevada and Pennsylvania among them — and the District of Columbia. Romney would lay claim to 206, from probable victories in 24 states that are strong Republican turf or tilt toward the GOP, including North Carolina.

Up for grabs are 83 electoral votes spread across Colorado, Florida, Ohio, New Hampshire, Virginia and Wisconsin.

Of those, Republicans and Democrats alike said Obama seems in a bit better shape than Romney in Ohio and Wisconsin, while Romney appears to be performing slightly better than Obama or has pulled even in Florida and Virginia.

The AP’s analysis is not meant to be predictive, but instead to provide a snapshot of a race that has been extraordinarily close from the outset. The analysis is based on interviews with more than a dozen Republican and Democratic strategists in Washington and in the most contested states; public polls; internal campaign surveys; early vote figures; spending on television advertising; candidate travel; and get-out-the-vote organizations.

Both Republicans and Democrats said Tuesday’s election has tightened across the board the homestretch. Many factors are adding to the uncertainty, including early vote tallies, Election Day turnout and the impact of Superstorm Sandy in the East. There’s no telling the impact of Libertarian Party candidate Gary Johnson, who’s on the ballot in 48 states, including all the battlegrounds, or Virgil Goode, an ex-congressman from Virginia who’s running on the Constitution Party ticket.

But here’s perhaps the biggest issue complicating efforts to get a handle on where the race really stands: different assumptions that each party’s pollsters are making about the demographic makeup of the electorate. Republicans are anticipating that the body of voters who end up casting ballots will be more like the 2004 electorate, heavily white and male. Democrats argue that 2012 voters as a whole will look more like the electorate of four years ago when record numbers of minorities and young people turned out.

The difference has meant wildly disparate polling coming from Republicans and Democrats, with each side claiming that it’s measuring voter attitudes more precisely than the opposition.

Said Republican strategist Phil Musser: “The conviction with which both sides say they are on a trajectory to victory is unique.”

Tuesday will determine which side is correct. For now, the gulf between the two sides’ polling has made it difficult to judge which candidate is faring better in the six up-for-grabs states.

In the final hours of the campaign, national polls show a neck-and-neck race for the popular vote.

But it’s the Electoral College vote that elects the president. In that state-by-state race, Obama long has had the advantage because he’s started with more states — and votes — in his column, giving him more ways to cobble together the victories he needs to reach 270. Romney has had fewer states and votes, and, thus few paths — though victory remained within his reach.

Said Mo Elleithee, a Democratic strategist who specializes in Virginia: “A 1 percent shift in any demographic group in Virginia is the difference between Barack Obama and Mitt Romney being president. That’s how close this election is.”

Over the past month, Romney’s standing in national polls improved following strong performances in the October debates, and he’s strengthened his position in several states, including Colorado, Florida and Virginia.

But all three are too close to call and both Romney and Obama had final weekend campaign appearances in them, underscoring their fluidity. Romney has gained ground in North Carolina, which now is tipping his way. Obama’s team has all but acknowledged that it’s the weakest for the Democrat of the competitive states, and the president himself isn’t visiting the state in the final stretch.

But the key for both campaigns is the Midwest, specifically Ohio. It offers 18 electoral votes and figures prominently in each strategy. That urgency was evident by the multiple visits to the state by each candidate in the final days.

Obama has enough of an edge in the electoral race that he could win the White House without carrying Ohio. But it’s hard to see how Romney does so.

That assessment, and Obama’s slight but stubbornly persistent edge in the state, could explain why Romney made a late-game play for Democratic-leaning Pennsylvania’s 20 electoral votes. He began advertising heavily in the state last week and put a stop in Philadelphia on his Sunday schedule even though the state has voted for a Democratic presidential nominee in every election since 1988.

Democrats projected confidence about holding Pennsylvania, although Obama responded with his own ads in the state and was sending former President Bill Clinton to campaign for him there on Monday.

Not that Romney is writing off Ohio. No Republican has won the White House without winning the state, and, without it, Romney would need a near sweep of the other battleground states.

“Ohio, you’re probably going to decide the next president of the United States,” Romney said Friday at a plant near Columbus.

Refusing to cede ground in Ohio, Obama’s campaign is flooding the state with four visits in as many days to every major media market by the president, first lady Michelle Obama, Vice President Joe Biden and Clinton. Obama planned to finish campaigning in Ohio on Monday at a Columbus rally with rocker Bruce Springsteen.

Obama’s team was projecting confidence in Ohio, arguing that the renewed debate in the final weeks over the auto industry financial bailout — which Obama signed and Romney has criticized — has boosted the president at the right time while undercutting Romney. Republicans in the state don’t dispute that characterization, and Obama has kept the heat on Romney over a TV ad he’s running that misleadingly suggests that the auto bailout helped U.S. auto giants send jobs to China.

“This isn’t a game. These are people’s jobs. These are people’s lives,” Obama told a raucous crowd in Friday in a Columbus suburb. “You don’t scare hard-working Americans just to scare up some votes.”

Wisconsin, the home state of GOP vice presidential nominee Paul Ryan, also figures prominently in the calculations for both sides, but, again, is more critical for Romney, who is looking to stop Obama in the Rust Belt.

Here’s why: Obama surest path to a second term cuts through both Ohio and Wisconsin, and victories in those states would give him 271 electoral votes as long as he wins all of the states that are solidly Democratic or tilting his way.

Those include:

• Iowa, where public and internal campaign polls shows Obama with an edge even though Romney has campaigned in the state a half-dozen times in the past two weeks and has spent the final hours of the campaign working to narrow Obama’s edge in early voting. Both candidates were in Iowa on Saturday, and Romney was back Sunday playing hard for late-deciders his team is confident will break their way and make the difference.

Obama planned to return to the state Monday. Republicans characterized that visit as a sign of instability while Obama’s team said he wanted to end his campaign in the state whose 2008 caucuses put him on the road to the presidency.

• Nevada, where Republicans and Democrats said the president has gained ground over the past few weeks, despite high unemployment and foreclosures. Obama seems to be benefiting from the state’s large Hispanic voting bloc and political machinery of Senate Majority Leader Harry Reid.

Romney all but acknowledged the president had an edge in the states. He scrapped plans to visit the state in the final two days. Instead, he sent Ryan.