William Douglas Washington Bureau

NORTH CAROLINA (15 electoral votes)

Republicans were so certain of carrying the Tar Heel State last time that South Carolina Republican Sen. Lindsey Graham boasted: “I’ll beat Michael Phelps in swimming before Barack Obama wins North Carolina.”

After Obama improbably carried North Carolina in 2008, Republicans are making no such boasts this time. This summer, the state has endured a $50 million advertising barrage, with Romney and his allies outspending Obama by more than two to one.

So far, the ad war has barely moved the polls, with most showing the race within the margin of error. But Democrats acknowledge they face an uphill task in a state with the fifth highest unemployment rate in the country.

Obama is counting on a massive grass-roots effort and a boost from the convention that concluded Thursday in Charlotte, and from an influx of new residents from more Democratic-leaning parts of the country.

Rob Christensen The News & Observer of Raleigh, N.C.

VIRGINIA (13 electoral votes)

Virginia was long regarded as a conservative Southern state. But in 2008, Obama became the first Democratic candidate to carry the commonwealth in 44 years after putting together the broadest state political organization in modern times.

Republicans are fighting hard to get the state back, and Virginia is now among the most volatile of the swing states.

Democrats have made inroads in northern Virginia, where the population has boomed in recent years, particularly with minorities and younger voters. Republicans have electoral strength in the Shenandoah Valley and rural south and southwestern Virginia.

The key battleground areas are the outer suburbs of Washington, including Prince William and Loudoun counties; Hampton Roads, the sprawling region in southeastern Virginia and home to a large number of veterans, college students and African-Americans; and suburban Richmond.

Anita Kumar Washington Bureau

NEVADA (6 electoral votes)

Four years after Obama won Nevada by more than 12 percentage points, this recession-weary state — perhaps more than any other — tests his argument that the economy has improved on his watch.

Foreclosures are rampant and the unemployment rate still hovers around 12 percent, highest in the nation. The Republican Party, outnumbered by more than 100,000 active voters in 2008, has reduced the Democratic Party’s advantage to fewer than 60,000 active voters this year.

Yet a strong following for Rep. Ron Paul of Texas, evident at the Republican National Convention, and before that at a disorderly state convention, has forced Romney to work around the state party.

The state’s growing Latino population and large Mormon population could factor heavily in the outcome, likely helping Obama and Romney, respectively. David Siders The Sacramento Bee

NEW HAMPSHIRE (4 electoral votes)

Obama won the state soundly in 2008. Romney, who has a summer home in the state and was governor of neighboring Massachusetts, is hoping for a hometown edge.

The Granite State’s major claim to political fame stems from its first-in-the-nation presidential primary, which provides every candidate with a roadmap of the state’s political landscape. But it’s also a tempting prize in the general election, with an electorate so closely divided that it’s almost always up for grabs.