First impressions are important in politics, and no one has introduced himself better in the campaign for the Republican presidential nomination than businessman Herman Cain.

Cain has surged in just about every national or state poll this month, to the point that he is now in a virtual tie with former Massachusetts governor Mitt Romney, who many consider the front-runner. The latest CBS-New York Times poll put Cain ahead of Romney, though within the margin of error. A Quinnipiac University poll of Ohio voters showed him narrowly ahead of Romney. Texas Gov. Rick Perry, once seen as the strongest challenger to Romney, ran fifth in both surveys.

Cain is not the first Republican challenging Romney to see an abrupt increase in his support. Perry experienced the same thing when he joined the contest in August and declared himself the authentic conservative in the race. Before that, Rep. Michele Bachmann (Minn.) suddenly looked like a force after a strong performance in her first two debates.

Cain’s rise has been all the more surprising, however, because it has come after a series of debate performances, not just a single memorable moment in his campaign, after longer exposure to Republican voters, and despite some gaffes and mistakes. The Gallup organization reported this week that Cain is still the most positively viewed of the GOP candidates, by a wide margin.

The questions many Republicans are now asking: What is behind his sudden success? And can it last? Two hours of revealing conversation among a dozen Ohioans at a focus group here Monday night suggested answers to both.

Pollster Peter Hart moderated the discussion, the first in a series of 2012 focus groups he will conduct for the Annenberg Public Policy Center at the University of Pennsylvania. Like any focus group, this one did not represent a scientific sample of the electorate. But in the context of recent polls, the participants brought into sharper relief the reasons that Cain has surged, and the obstacles that remain.

Moving at a rapid pace, Hart coaxed from the group of Republicans, Democrats and independents their feelings about the state of the country (gloomy), their view of Washington (totally negative), their assessment of President Obama (generally disappointed, even among most of those who backed him) and what they are looking for in 2012.

What was most striking was the genuine interest expressed in Cain and his candidacy. Time and again he rose to the top of the conversation about the Republican candidates. He was described in far more positive terms than either Perry or Romney. When Hart asked the group who intrigued them most right now, no one came close to Cain in the number of mentions.

Confirming Gallup polls, Cain was viewed as the most likable of the candidates, a people person, a hard-working businessman, a potential problem-solver and someone who many said would be a good neighbor. “He’s Main Street,” said Becky Leighty, a Republican. “He’s not Wall Street, and he’s not a politician.”

At one point, Hart asked the participants to think back to fifth grade and the types of students they had encountered. From a list that included descriptions such as “teacher’s pet,” “loner,” “hard worker,” “nerd” and “know it all,” Hart asked them to write down which most applied to Cain, to Romney, to Perry and to Obama.

The majority described Cain as the classmate who was the “hard worker,” with others saying he was the “all-American kid” or “the kid everyone respects.”

In contrast, Perry left this group cold. If he is the person many GOP strategists believed was destined to challenge Romney for the nomination, no one had given that memo to these Ohioans.

In the fifth-grade exercise, eight of the 12 wrote down “bully” as the kind of kid he reminded them of. When the discussion turned to other attributes, he was described as the kind of neighbor others would not want to mess with, or someone who would build a fence around his property, or someone who would be in everybody else’s business.

“He wouldn’t be on the casserole committee,” said Sydney Mathis, a Democrat.

“Annoying,” said Lisa Cedrone, an independent voter who supported Obama in 2008 and is undecided today.

The negative descriptions of Perry underscored the depth of the problems the Texan has created for himself after 10 weeks as a candidate. His decline has created the vacuum that Cain is filling. That may be one reason that Perry’s opening ad in Iowa, released Wednesday, is wholly positive and almost vanilla in character. More than any other candidate, he needs a new introduction to Republican voters.

Romney fared somewhat better than Perry. He was seen by a few as the GOP candidate best prepared to be president. Some described him as the toughest, based in part on his toe-to-toe exchange with Perry at the Las Vegas debate.

But Romney also was described in terms that set him apart from ordinary people. In fifth grade, he would have been the “rich and privileged kid,” five in the group said. He was described as someone from Park Avenue or Wall Street. Others saw him as overly political (“chameleon” and “pompous” were two other words used).

The group’s comments were a reminder of just how many Republicans have resisted embracing Romney’s candidacy, and why they are not ready to support him. That has kept the GOP race fluid all year and continues to do so.

Cain is riding a wave of good feeling, in part because of who he is and how he presents himself, and in part because of the other candidates’ perceived weaknesses. Right now, some of the Ohioans in the focus group were willing to cut him some slack on the questions being raised about his “9-9-9” tax plan, although they acknowledged that they didn’t know enough about it to pass judgment.

“I’m not sure it’s realistic or something that could be implemented easily,” said Jennifer Sharm, an independent who leans toward the GOP. “But I think it’s novel. . . . The system is broken, and we need a major fix.”

Toward the end of the evening, Hart sat down at the table and braced the group with perhaps the most telling question of the night for Cain’s candidacy. “Here’s what I don’t get,” he began. He noted that Cain had been described as down to Earth and a good neighbor, but he also recalled how the group had described the country as being in terrible shape and noted that Cain is running a campaign with little staff or infrastructure.

“Do you think this person could be president of the United States?” he asked. “Is anybody willing to raise your hand and say, ‘I would be comfortable if he became the next president of the United States?’ ”

Not a hand went up. Two people said they would want to know who Cain’s vice presidential running mate would be. Four said they would feel as comfortable with Cain as with Obama, but they were all Republicans eager to see an end to the Obama presidency.

For all the good impressions Cain has made, he still must cross a threshold in the minds of rank-and-file Republicans — and, if he were to become the nominee, in the minds of the many undecided independents.

If voters can begin to see him in the Oval Office, his candidacy will have taken a dramatic turn. That is what the next few months will answer. What this sample of Ohioans was saying Monday night was that he remains several steps short of that goal.