(FORTUNE Magazine) – SITTING ACROSS FROM MARK WARNER ON TINY cafeteria stools at the Samuel Tucker Elementary School in Alexandria, I pop the question that everyone has been asking the Virginia governor since, oh, about 3 P.M. on Wednesday, Nov. 3: Do you want to be President? The desired qualifications listed on the Democrats' latest want ad aren't hard to divine: Given what happened on Election Day, maybe next time the party needs a (1) Southern (2) governor with (3) a record of business success--the kind of guy who (4) won by seven percentage points in Southern counties where George Bush beat John Kerry by 17.

Warner, a trim, young-looking 50-year-old who still plays basketball with buddies a few times a month, demurs, saying he wants to be "the best governor I can be" in his last year in office. It's the right answer, of course; the question is premature. Still, I'm spending the morning with Warner to get a sense of how the suit might fit.

Warner has an impressive story. The first in his family to graduate from college (George Washington University, Harvard Law), Warner co-founded the venture capital firm Columbia Capital and was an early investor in Nextel. After he amassed a fortune now worth $180 million, the political bug returned (Warner worked briefly for the DNC after law school). He lost a Senate race in 1996 to John Warner (no relation) before winning the governorship in 2001.

Having walked right into a post-bubble budget hangover--Virginia, as did most states, spent a good part of the 1990s enacting unsustainable tax cuts and spending increases--Warner spent two years slashing budgets and state jobs. But when he introduced the state's first six-year budget forecast, the "outyears" still showed red ink. The problem had become structural. Unlike many pols, however, Warner didn't paper it over.

Instead, he became the "PowerPoint governor," crisscrossing the state with his laptop slide show on the commonwealth's woes and his plan to fix them--a plan that included hefty tax hikes, even as it boosted investment in areas like education. When the dust cleared, Warner had joined forces with the Republican-controlled legislature to pass long-term reforms that landed him and his chief GOP partner on the cover of Governing magazine as "public officials of the year." His 49 peers around the country picked him to head the National Governor's Association. Today Warner's approval ratings--and remember, this is after a tax hike in a conservative state--hover in the low 60s.

Warner seems to get most energized when he talks about education and improving the way government actually runs. "We put the least experienced and most underperforming teachers in the worst schools," Warner says, explaining his efforts to buck this trend. He's lifted efficiency and effectiveness in areas from procurement to real estate management; consolidated dozens of government data-processing centers under one roof; and set up educational SWAT teams that help schools drive more dollars into classrooms. Warner also has some advice for his party.

"There was never any break with Democratic orthodoxy," says Warner of the Kerry campaign. "Whether we like it or not, in maybe two-thirds of America you've almost got to show you're not a 'national Democrat.'" Bill Clinton did that, he says. Warner did it in his own campaign--by stumping at NASCAR races and bluegrass concerts, and by courting rural voters and gun owners without liberal condescension. It may not be fair, Warner says, but Democrats must convince Southern voters they're not Ted Kennedy before folks are "even willing to listen to the rest of it."

When voters do get to "the rest of it," Warner's bona fides as a self-made entrepreneur are an asset. When unassailable capitalists like Bob Rubin or Jon Corzine or Mark Warner talk about how government can help poor kids get ahead or cover the uninsured, Republicans can't credibly cast them as Marxists.

Still, they can cast Warner as a tax-hiker. That, and the governor's low-key persona, may be his biggest challenges as he mulls a bigger stage. While Warner's earnestness and smarts are appealing, you don't get the "this guy's gonna be President" vibe Bill Clinton had.

But by 2008 voters may have a different steak-to-sizzle ratio in mind--especially when it comes to the grownup conversation the country needs on how to square the cost of the baby-boomers' retirement with other priorities. To date the dishonesty has been breathtaking, exemplified by White House talk of using trillions in fresh, off-the-books debt to fund Social Security reform. If these charades continue, a pragmatic governor who's shown he can work across the aisle and lead citizens in an honest discussion about the choices we face may be just what the nation is looking for.

MATT MILLER (www.mattmilleronline.com) is a senior fellow at the Center for American Progress and the author of The Two Percent Solution: Fixing America's Problems in Ways Liberals and Conservatives Can Love.