WESTERVILLE, Ohio — President Barack Obama and Mitt Romney are plunging into the final nine days of a multibillion-dollar presidential race focused not only on the seven most competitive states, but also on battleground counties within them that could determine an exceedingly close contest.

They include the suburbs here in Franklin County, Ohio, where many young married women turned to Obama in 2008 out of frustration with the wars in Iraq and Afghanistan but who could turn against him now for perceived failures on his campaign promises and a slow-to-recover economy.

In Colorado, it is Arapahoe County, where Romney’s campaign is courting Hispanic business owners who are frustrated with the national health care law. It is Hillsborough County in Florida, where both sides agree that whoever wins the independent voters is likely to be president.

Obama now has a solid lead in states that account for 185 electoral votes, and he is well positioned in states representing 58 more, for a total of 243, according to a ranking of states by The New York Times, based on polls and interviews with strategists in both campaigns.

Romney has solid leads in states with 180 electoral votes and is well positioned in states with 26 more, according to the Times rating, for a total of 206. It takes 270 electoral votes to win the presidency.

In the closing days of the race, seven states representing 89 electoral votes — Colorado, Florida, Iowa, New Hampshire, Ohio, Virginia and Wisconsin — are now considered tossups. Here is a look at their dynamics and the potential path for each candidate.

Florida

Romney’s planned swing through Florida on Saturday — the first day of in-person early voting there — was to include a visit to a Republican county in the Panhandle where he wants to pump up his vote count (Escambia), a Democratic county where he wants to cut into Obama’s expected lead (Osceola), and a swing county (Pasco).

For good reason.

Romney cannot afford to leave any base untouched. If he loses Florida, his chances of winning the presidency depend on sweeping nine other states, including Ohio and Nevada.

Florida has been considered challenging territory for Obama all year. Even when polls have shown him ahead, both campaigns have expressed skepticism that the edge would hold.

But at Obama’s headquarters in Chicago, his aides said in interviews last week that they believed they had at least a 50 percent shot in Florida.

Republicans, still bullish about victory, say Romney can rely on a very strong showing in Polk County, a Republican stronghold, and edges in the swing county of Hillsborough as well as in Volusia County, home to Daytona and New Izmir Beach.

New Hampshire

On Obama’s scheduled trip on Saturday to Nashua, N.H., with the singer James Taylor in tow, he will be wooing a state that revels in its reputation for unpredictability.

Obama won every county there in 2008, a feat that even Bill Clinton did not pull off in 1992 and 1996. But Obama’s sometimes comfortable lead in polls has dwindled.

Romney’s aides have been somewhat optimistic about his chances in the state. He was the governor in Massachusetts next door, and he vacations there. His lakeside home in Wolfeboro is in Carroll County, which he will need to win.

He and his campaign have plied the state’s two traditionally Republican-leaning counties in southern New Hampshire — Rockingham and Hillsborough — with attention since he announced his run for the presidency (in the Rockingham town of Stratham).

New Hampshire has only four Electoral College votes. But they would make all the difference if Romney also wins Florida, North Carolina, Virginia and Ohio and Obama takes Nevada, Colorado, Iowa and Wisconsin.

Colorado

There is a potential outcome that has tantalized political addicts everywhere: that Colorado will become the new Florida, the state that decides it all.

For it to come to that, Romney must win four of the most competitive states — New Hampshire, Virginia, Florida and Wisconsin — leaving Obama with Ohio and Iowa. That would give Romney 262 Electoral College votes to Obama’s 267, leaving both in need of Colorado’s nine. In 2008, Obama became the first Democrat to win the state in 16 years by stealing the counties north and south of Boulder — Jefferson and Larimer — and Arapahoe County near Denver and by shaving down the Republican margin in conservative areas like Colorado Springs.

A Wall Street Journal/NBC News/Marist College poll released Thursday showed Obama and Romney to be tied among likely voters in the state.

Iowa

No state among the battlegrounds is more sentimental and symbolic to Obama. Iowa christened his presidential candidacy in 2008; his victory in the caucuses there helped pave the way to his winning the Democratic nomination.

Iowa’s unemployment rate is significantly lower than the national average, but Obama has campaigned in the state as if his candidacy depended upon it. And perhaps it does.

Romney is looking for backup options if the battleground map does not tilt his way. And the six electoral votes in Iowa could be a critical piece to that puzzle.

The suburban areas around Des Moines (Polk County) and Davenport (Scott County) are crucial for both candidates.

Social conservatives are working to deliver a record turnout in northwestern Iowa. Democrats are taking steps to keep outpacing Republicans in early voting, which means Romney will have to deliver a strong performance on Election Day to win. Four years ago, Obama received fewer votes on Election Day than Sen. John McCain, but still carried the state because of the ones he banked early.

Ohio

Romney spent four of the last five days in the state trying to break through with middle-class voters, making the case that the recovery under Obama has been inadequate. With 18 electoral votes at stake, both candidates are treating the state as if they were running for governor. To win, Romney needs added strength in rural and suburban areas, where Obama drew more support in 2008 than did previous Democratic candidates. Late last week, Romney held a rally in Defiance, Ohio, in a Republican-leaning county, one where he needs the margins to return to the levels seen in 2004.

The results in Cincinnati, in Hamilton County, will be among the closest watched in the country. The county supported Obama in 2008 — the first time a Democrat won in four decades — and is one of the most highly-competitive this year.

“You want to peak at the right time, and we are peaking at the right time,” said Chris Jennings, the Ohio campaign manager for Romney.

Virginia

Virginia is vital to almost every one of Romney’s paths to the White House if he does not win Ohio, which explains why he has spent so much time visiting the state, including two planned rallies today (a third, in Virginia Beach, was canceled because of Hurricane Sandy).

Obama was the first Democrat to win the state since 1964. The tide he rode among black voters in places like Hampton, on the coast, is likely to roll again. And the northern part of the state, in the Washington area, is still considered Obama country.

Romney has focused much of his effort in areas like those around Norfolk, heavily populated with military personnel, where he asserts that Obama has allowed the Navy to wither, and in coal-mining country in the south, where he portrays Obama as hostile to the industry and quick to impose costly regulations on business.

A run of polls in the late summer showed Obama to be on his way to establishing a real advantage, but in recent weeks the race has fallen into an effective tie. Romney’s improving standing among undecided female voters after the debates — which he stoked with an advertisement that sought to soften his stance against abortion — made Obama’s aides especially nervous.

Wisconsin

The 2008 presidential election, when Obama carried the state by 14 percentage points, is a distant memory. The electorate is far more polarized this year, particularly after the contentious recall attempt of Republican Gov. Scott Walker in June, which failed.

One factor is the pride that comes from a native son, Rep. Paul D. Ryan, on the ticket. His hometown, Janesville, is a strong Democratic-leaning city, so any votes he wins from there could help the Republican margins in a race that both sides agree seems more like 2000 and 2004, when George W. Bush lost by only a sliver.

The Romney campaign does not consider Wisconsin one of its best prospects, but a victory would break the Midwestern firewall that Obama is trying to build. And if Romney could win the state’s 10 electoral votes — coupled with Colorado’s nine — it would counterbalance a potential loss in Ohio.