He had received a phone call just that morning from a supporter furious about yet another newspaper story suggesting that he was boring. It was not the best of days for Sen. Rob Portman of Ohio, a man thought to be on Mitt Romney’s list of possible running mates. “I told my staff that I’m so boring that I didn’t even know I was boring,” he said at a large conference table, surrounded by several expressionless members of his staff.

He calmly turned and smiled at them.

The first rule for anyone interested in becoming a vice presidential nominee is that you can’t appear to be interested in becoming a vice presidential nominee. A corollary is that you should never seem to be very upset over criticism about your perceived lack of charisma or any other quality that might aid a vice presidential nominee, lest you look interested in becoming a vice presidential nominee. The whole pursuit is a real headache.

“However the press wants to characterize it is fine,” Portman said, and smiled again.

For weeks, Portman’s name has been among those at the top of Republican vice presidential possibilities. For weeks, ever since he played a vital role in aiding Romney narrowly beat Rick Santorum in the Ohio primary, the buzz about Portman’s status in the vice presidential sweepstakes has been intense, much of it fueled by theories about how he might help Romney, the presumptive Republican nominee, carry this critical swing state against President Obama.

But the standing of a potential running mate is like a volatile stock. Amid the frequent ups and downs of the speculative process, this day was certainly a downer for Portman. That morning, the Wall Street Journal had become the latest media titan to observe that, although the 56-year-old has a substantial governmental résumé, he suffers from a shortage of pizazz.

A week earlier, on his television show, Stephen Colbert had declared that a Romney-Portman ticket would amount to “the bland leading the bland.” One description of Portman in the Wall Street Journal article particularly nettled the senator and some of his close friends: “dry as dust.”

A fuming friend who called Portman that morning immediately launched into a denunciation of this characterization. “I said to him: ‘One, this is totally out of my control, out of our control — because it’s a unique process,’ ” the senator said. Then, he told his friend something else, just in case he or any other admirer might get the wrong idea: “But, second, my goal is not to become the vice presidential candidate but to help our country during this difficult time.”

‘It’s not about being exciting’

His friends and family members are never satisfied when he says things like that. They want him to talk about how he is a regular guy, a doer, exciting in his own way, with passions that include being a skilled kayaker and cyclist. They want him to talk about how he has kayaked the Yangtze and the Rio Grande, herded cattle on a ranch, shot the rapids in the Grand Canyon.

His older brother, Wym, remains annoyed about what Colbert said. “Flashy isn’t a word I’d use to describe Rob,” he said. “But when Colbert called him ‘bland,’ that just missed the point. . . . He’s not Obama or Clinton at the podium, but he’s a good orator, I think — he’s made a huge jump. What he’s always been is a thoughtful, serious person — I would think we would want that.”

Portman signaled that he didn’t much care about Colbert’s comment. “I mean, it was a surprise,” he says. “But it was fine. To me, it’s not about being exciting.”

His boosters deride the notion of “exciting,” trumpeting that his record is free of rhetorical gaffes and character blemishes, exactly what you want, they argue, from a running mate. They boast that Portman’s many government positions — including 12 years as a congressman to go along with stints as George W. Bush’s U.S. trade representative and director of the Office of Management and Budget — negate the kind of qualification issues that have bedeviled many vice presidential candidates, most recently Sarah Palin.

But Portman’s admirers know that other prospective running mates have been lavished with far more attention. As Portman sat in this Columbus conference room, the grinning visage of New Jersey Gov. Chris Christie flooded cable news, following a casual remark Christie made the day before that Romney might be able to persuade him to be his running mate. In New Hampshire, Romney showed off the state’s Republican freshman senator, Kelly Ayotte, who also is considered a vice presidential possibility. A week earlier, Romney had squired around a young Republican star, Sen. Marco Rubio of Florida, who later delivered a much-ballyhooed foreign policy speech at the Brookings Institution.

Rep. Paul Ryan of Wisconsin and Virginia Gov. Robert F. McDonnell had also emerged as fixtures in the vice presidential discussion, with Ryan especially portrayed as a kindred spirit of Romney’s, someone able to finish the top man’s sentences and make him laugh. Romney and Ryan had met privately last autumn to talk about economic policy and deficits, said someone close to the candidate. Although Portman, he added, was “much admired” by the Romney team and remained very high on the VP list, the view among several Romney insiders was that the chemistry between their leader and Portman “had not been great — not bad, he’s a nice guy, but just not great.”

Still, only one man knows Portman’s standing for certain. And Mitt Romney isn’t saying anything about the process. “Senator Portman is a proven leader and a trusted fiscal conservative,” says Ryan Williams, a Romney campaign spokesman. “He played an important role during Governor Romney’s successful primary campaign in Ohio.”

Portman remains as disciplined and self-effacing as ever. Asked the same question that was put to Christie the day before about whether he would accept the vice presidential nomination, Portman declined to take the bait. He paused. No political figure can pause longer or answer more deliberatively than Portman. Icebergs could form in his cool hesitation. “I don’t know,” he said finally. “My sense is . . . [lengthy pause], given all the various . . . [lengthier pause] . . . candidates he’s looking at, that it’s unlikely that question will ever be posed. He’s got some great candidates.”

Sparring partner

Those close to Portman wish he would promote himself more. It’s not in him, says a friend, who adds that the senator would be perturbed if he knew he had said that much. The friend notes that, in March, Portman did not want anyone talking about his role in a search for a missing 16-year-old boy who had been last seen walking along a road running parallel to a river near Portman’s neighborhood in Terrace Park, a suburb of Cincinnati.

Portman drove several hours back to Terrace Park from a speaking engagement, called some friends, and the group set out in kayaks on the Little Miami River toward the Ohio River, looking for the boy, who attended the same high school as Portman’s daughter, Sally. The teenager, Collin Barton, was ultimately found dead along an embankment near the road, having been struck by a passing car.

Portman, a father of three with his wife, Jane, had been initially reluctant to talk about the matter on the record. Choking up and teary-eyed, he brought his hand to his face. “This boy was in my daughter’s class,” he said, finding it difficult to go on.

He had many reasons for not wanting to talk about it — the issue of sensitivity to the family being chief among them. But he also did not want to be seen as exploiting a tragedy. Everything he and other vice presidential prospects uttered was fodder for character analysis and political danger. Sometimes merely talking about good deeds is playing with fire. Portman wanted to make it clear that he had not raised the subject.

His aides sat silently. Minutes after a speech Portman had delivered at Ohio State University on energy issues, they had brought him here to this campus conference room, away from a pack of local reporters whose numbers had steadily grown since the vice presidential buzz began.

He had begun his political climb as a hardworking subordinate operating in neatly appointed rooms much like this one. A young trade lawyer steeped in Republican politics, he honed policy ideas for the administration of George H.W. Bush as an associate White House counsel. Soon, he rose to become the president’s chief liaison to Congress, as director of the White House Office of Legislative Affairs.

In no small part since, he has ascended on the strength of his connections to two different Bush administrations. During the 2000 presidential campaign, the staff for then-Texas Gov. George W. Bush asked him to play the part of Democratic vice presidential candidate Joseph I. Lieberman in mock debates that the Bush team had arranged for Richard B. Cheney, its desired running mate. Portman proved so formidable that, before the last of Bush’s three debates, he found himself in the dining room of the Texas governor’s mansion, playing Al Gore against Bush. He had prepared for the practice session by watching tapes of virtually every Gore debate he could find.

“There were only about a dozen of us in that room,” remembers the campaign’s policy director, Joshua B. Bolten, who would later become director of the Office of Management and Budget and Bush’s White House chief of staff. “Rob really threw some nasty jabs at [Bush]. Then, while [Bush] was answering a question, Rob nonchalantly walked up to him and invaded his space. Bush asked: ‘What are you doing?’ Rob said something like, ‘I’m coming into your space.’ ”

Bush shook his head. “Gore’s never going to do that.”

“He might do it,” Portman said. “He’s done it in other debates.”

Days later, in the real debate, Gore rose from a stool and walked toward Bush. Ready for it, Bush did a mock double-take and smiled dismissively at him.

In 2008, Portman served as a sparring partner for John McCain during a presidential debate practice, playing the role of Barack Obama. A Portman friend recalls receiving a phone call from a glum McCain aide shortly after a mock debate ended. “Portman just annihilated our guy,” the aide said. Adds former McCain strategist Steve Schmidt, who also watched the practices: “Anybody who saw Rob Portman in the role of Barack Obama during debate preps has no doubt about his ability to compete, debate and campaign effectively at the highest levels.”

An Ohio political friend says that Portman made no secret during a private discussion between them of his desire to be invited onto the ticket. “He is not running for the vice presidency — he knows that you can’t do that,” says the friend, who spoke on the condition of anonymity because he still has dealings with Portman’s office. “He knows there is really nothing that can be done between now and the convention. All you can do is carry out the assignments given to you by the nominee and let the process unfold.”

Even if Portman and his camp do everything right, they know the big invitation might never come. His close friend Bolten wonders whether Portman’s long congressional history and his links to the capital’s powerhouses could be an impediment in a year in which everyone, in both parties, seems eager to run against Washington. “It may imperil his chances of being picked,” Bolten observed. “I don’t think his [connections] particularly help him right now in a campaign dynamic. Enough said.”

Meanwhile, trying to dampen such discussions, Wym Portman added that, although his brother “is taking the attention seriously, it’s no slam-dunk” that he would even accept the second spot.

In the quiet conference room, the subject of all the worries did nothing to discourage the uncertainty. “As Wym said, I’m not sure this is the right opportunity for me,” Portman said.

If Romney asks you, you’re really saying you don’t know?

“I’d have to then get much more serious about it,” he replied.

Such is the vice presidential non-pursuit pursuit.

“It’s all” — he paused, a very long pause — “very unusual.”