(Image credit: Tony Dejak/AP Photo)

Important as Ohio is for Mitt Romney and Rick Santorum Tuesday, it's  doubly critical for President Obama come November - a fact underscored by Democrats' quiet but aggressive Buckeye State shadow campaign.

Eight months before Election Day, Obama for America is operating at full tilt in Ohio, with a dozen paid staffers overseeing  nine field offices across the state, with several more expected to open in the next few months, a campaign official said. The 10th Obama office opens Thursday in Youngstown.

When Republican primary voters cast ballots today, Democrats will be manning phone banks and recruiting volunteers for  "neighborhood teams," according to postings on the Obama-Biden website.

Obama volunteers have already held more than 5,000 organizing events in Ohio since April, engaging more than 650,000 voters, the campaign said.

They're using the primary "as a way to sort of oil the machinery for Obama in the general election, which is really smart," said former Michigan Gov. and Obama surrogate Jennifer Granholm. "They have people on the ground everywhere in every state."

The president's campaign has also been on the air in Ohio, running a positive 30-second TV spot touting Obama's record on ethics and energy, while campaign staff have held conference calls and published memos attacking Romney on the auto bailout, tax cuts  and manufacturing and trade policy.

"Mitt Romney has not been honest about his record on the campaign trail, and it's certainly our responsibility to point out the inconsistencies," said Obama campaign spokesman Ben LaBolt, explaining the offensive.

As for whether the efforts include an attempt to meddle in the semi-open Ohio GOP primary - encouraging Democrats to  vote for Santorum, who's seen as a weaker general election candidate - Democrats insist that's not part of the plan.

"In states across the country, there are Democratic candidates on the ballot and those are the folks we're encouraging our supporters to support," LaBolt said.

From Alaska, where voters caucus today, to Massachusetts and Georgia, all holding primary votes, Democrats are exercising the same plan in something of a dry run for November.  But none of the 10 Super Tuesday states is more important than Ohio.

No candidate for president since 1960 has won the White House without carrying Ohio. And while Obama carried the state with 52 percent of the vote in 2008, polls show him now locked in a dead heat with likely GOP nominee Mitt Romney.

The most recent Quinnipiac University poll of registered Ohio voters shows Obama virtually tied with Romney - 46 to 44 percent - but holding a slight edge among independent voters, 45 to 41 percent.  The poll, which was conducted Feb. 7-12, has a margin of error of 2.6 points.

Obama's job approval remains underwater at 47 percent, but the figure is a slight improvement for the president, who received  44 percent approval a month earlier, according to the poll.

Still, Republicans see Ohio as increasingly red turf, their hopes buoyed by Republican John Kasich's 2010 victory over incumbent Democratic Gov. Ted Strickland for the state's top post, and a successful 2011 ballot measure rejecting part of the Obama health care law.

They also say high unemployment (7.7 percent in Ohio in January) and skyrocketing federal deficits are also factors that have energized Ohio's conservative grassroots and boosted enthusiasm for an Obama alternative.

"While Obama is spending time going to key coalitions he's lost over the past three years, from youth voters to women and independents, to shore up his base, we're going to be able to jump right into making the case against Barack Obama," said Republican National Committee spokeswoman Kirsten Kukowski.

"Between higher unemployment, the failed stimulus, record debt, unpopular Obamacare and doubling gas prices under his watch, Ohio voters are going to take a lot of convincing," she said.

Obama last visited Ohio on Jan. 4 - the day after the Iowa caucuses - for an economic speech aimed at portraying himself as a "warrior for the middle class." Vice President Joe Biden and first lady Michelle Obama have each visited the state for official and political events as recently as last month.