Mitt Romney faces a narrow path to the presidency, one that requires winning back states that President Obama took from Republicans in 2008 and that has few apparent opportunities for Romney to steal away traditionally Democratic states.

Months ago, Obama’s campaign advisers laid out five distinct ways for the president to clear the threshold of 270 electoral college votes and win reelection. As Romney, the presumptive Republican presidential nominee, and his advisers chart their strategy, they plan to target a dozen to 15 states and say that they, too, have more routes than their opponents claim.

But Romney’s team acknowledges that any realistic course to 270 starts with winning back three historically Republican states that Obama won in 2008 — Indiana, North Carolina and Virginia — and believes that changing demographics in Virginia present a challenge.

After that, Romney must play take-away with the Democrats in a number of other states that the Obama campaign flipped to its column four years ago. The two biggest and most important are Ohio and Florida, which advisers see as must-wins for Romney unless he can pick off one of the 18 states that Democrats have won in each of the past five elections.

Romney’s advisers see two things in particular working to their advantage despite some of the geographic hurdles they face. One is the overall weakness of the economy, which they believe will ultimately decide the election, and the other is that enthusiasm within the Obama coalition is down from 2008.

“We’re going to spread the map as far as we can for as long as we can,” said Rich Beeson, the Romney campaign’s national political director. “I compare the map to something like molten lava. It just hasn’t hardened yet, it’s moving around, and it will continue to move around until the bell rings for the bell lap after Labor Day.”

Romney campaign officials point to Michigan as one of those traditionally Democratic states where they expect to compete hard, noting that it is the former Massachusetts governor’s home state. But some top Romney supporters scoff at those ambitions, arguing that Romney’s opposition to the auto bailout alone is a sizable hurdle to overcome there. Sen. John McCain of Arizona, the Republican nominee in 2008, abandoned the state in the face of his limited resources and low prospects of winning there.

If, however, Romney can win the three longtime Republican states and take back Ohio and Florida, he will need just one more of the states that Obama flipped in 2008 to get to 270. Romney advisers express optimism about their chances in two other states in Obama’s column in 2008, Iowa and New Hampshire. The Granite State is attractive because of its proximity to Massachusetts, where Romney served as governor. Iowa, which launched Obama in the caucuses in 2008, has become more problematic for the Democrats this year.

The Romney campaign’s thinking about the electoral map, detailed in interviews this week with top campaign officials and advisers at Boston headquarters, as well as several Republican strategists, is akin to the “3-2-1” strategy authored recently by Bush strategist Karl Rove. Under that strategy, Romney would need to win three traditionally Republican states (Indiana, North Carolina and Virgina), plus two perennial swing states (Ohio and Florida), then one more state from half a dozen tossups.

Among the tossups is a trio of Western states that Obama carried four years ago: Colorado, Nevada and New Mexico. At this early stage, Nevada appears the most competitive because the state’s economy has been decimated by the housing crisis. And Romney’s team is counting on high turnout by Mormon voters there.

But in all the Western battlegrounds (as well as in Florida), Romney’s weak numbers with Hispanic voters pose a serious obstacle. Campaign officials said they will begin to address the problem by focusing on economic issues in their messaging to the Latino community, believing that will overcome damage done during the primaries by Romney’s hard-line stance on immigration.

In each battleground, advisers said Romney hopes to erase Obama’s 2008 margins by appealing to GOP-leaning independents and moderate voters who populate the suburban rings surrounding big cities and who may have grown disillusioned with Obama.

Romney advisers see those voters as potentially helpful in several states, including Pennsylvania, another Democratic stronghold they are eyeing as a possible target. Romney rolled up big margins in many of the suburban “collar counties” on his way to primary victories in Michigan, Ohio, Illinois and elsewhere. The question is whether that will translate in a general-election match-up.

Yet there appear to be only a few ways for the Romney team to expand the electoral map beyond simply winning back states Obama captured from Republicans four years ago. Just as Obama’s campaign plans to compete in reliably Republican Arizona, Romney’s team boasts of possibly scrambling the electoral calculus by putting Michigan and Pennsylvania into play.

“Mitt Romney is a native Michigander, his dad was a three-term governor there, people are familiar with the Romney brand of leadership,” said Eric Fehrnstrom, a senior adviser to Romney.

Romney’s advisers recently briefed some top fundraisers on a Michigan plan that includes buying television ads and microtargeting voters — in particular non-college-educated white men — as well as devoting considerable “Mitt time,” meaning candidate visits, one fundraiser said.

But the fundraiser said he believes the effort may be merely a “head game” to scare the Obama campaign, saying Romney is weighed down there by his opposition to the federal auto bailout, widely seen in Michigan as a success. In 2008, Obama won Michigan by 16.5 percentage points.

Terry Holt, a top official in both of George W. Bush’s campaigns, said the Romney team would be foolish to devote too much time and money to Michigan, because he thinks there are better opportunities elsewhere, especially in the West.

“His roots in Michigan are not enough to override some of the political forces at work in Michigan,” Holt said. “It’s suffered the worst recession of any state in the country, but President Obama has a clear message there [that he saved the auto industry] and like it or not, that message is going to be like a drumbeat from now until the election.”

Inside Romney’s Boston headquarters, strategists — who have pored over polling and census data and studied state-by-state vote breakdowns from the past three presidential elections — say they see a number of ways for Romney to win 270 electoral votes.

But they acknowledge the difficult terrain. One top aide likened it to a skier at the top of a mountain. They can see the course, and no matter what moguls or sharp turns may exist, they are confident about pushing off.

“We definitely see a very clear path. We’re not overly confident, but we like our chances,” said the aide, who like some others interviewed was granted anonymity to speak candidly about strategy.

Their overall optimism is based on the assessment that Obama’s big electoral vote victory was predicated on the enthusiasm he generated in 2008, which they say is now largely gone. In states such as North Carolina and Virginia, for instance, Obama won in part by achieving vote edges among 18- to 25-year-olds, Hispanics and African Americans. But Romney’s strategists do not believe Obama can match those levels this year.

“They changed the composition of the electorate and they won by big margins,” said Romney pollster Neil Newhouse. “The problem in ’12 is there just isn’t the enthusiasm. The bloom is off the rose.”

The latest Washington Post poll shows Obama leading Romney by a significant margin in Virgina.

At the same time, Obama’s team is far ahead of Romney’s in staffing field offices coast to coast and mobilizing its grass-roots army to try to rekindle the magic of 2008.

Months ago, Obama’s campaign team unveiled five routes for the president to win at least 270 electoral votes. Each is predicated on Obama winning back some but not all of the swing states he carried in 2008, while one path has Obama picking up Arizona and losing Pennsylvania.

The Romney team is trying to catch up. This week the campaign announced the hiring of state directors in at least six swing states, with more expected soon.

As they decide where to deploy staff and allocate money, the leaders of Romney’s team are studying economic data. In economic misery, Romney sees opportunity, hoping to exploit voters’ anxieties in states such as Florida and Nevada, where the job and housing markets have been ravaged.

“Where the economic knife cuts the deepest and the angst is the deepest and the uncertainty is the deepest, that’s where the cult of personality is most shallow, and those are opportunities for us,” one Romney adviser said. “You tell me a place where unemployment is above 7.5 or 8 percent and the average length of time to sell a house is 180 days and those are places of opportunity.”