When President Bush heads to Mississippi tomorrow to tout his Social Security initiative, some Republicans hope voters see two men of presidential caliber: Mr. Bush and the state’s governor, Haley Barbour.

A small but influential group of GOP insiders are urging the former national party chairman to seek the Republican nomination for president in 2008.

“I would handicap the Haley thing seriously,” a GOP lobbyist in Washington, Mark Isakowitz, said. “Republicans around the country like him. They just like him. He’s been the face of our party for a long time. He’s built up a lot of goodwill. Now that’s he’s governor, it’s plausible,” Mr. Isakowitz said. “The keys to the kingdom always lie in being trusted by the base.”

Talk of a Barbour candidacy has increased decidedly in recent weeks, thanks in large part to the efforts of Ed Rogers, a partner in Mr. Barbour’s former lobbying firm. Mr. Rogers declined to be interviewed for this story, but he acknowledged that he recently registered two Web addresses – www.haley2008.com and www.haleyforpresident.com – to help keep Mr. Barbour’s presidential options open.

“There’s certainly a lot of Beltway chatter about it right now,” the executive director of the Republican Jewish Coalition, Matthew Brooks, said. “The level of volume has certainly been picking up.”

Mr. Barbour has been coy about the matter, disclaiming any interest in the presidency but stopping well short of an outright refusal to consider the job. “The governor has no plans to run for president,” a spokesman for Mr. Barbour, Peter Smith, said.

In a recent interview, Mr. Barbour, 57, jokingly brushed aside questions about his presidential aspirations. “Well, I could lose 50 pounds. I might even grow 4 inches. You never know,” he told the Associated Press. “But that’s not my intention.”

A friend of Mr. Barbour who is eager to see him run said interest in the idea picked up after it became clear that Governor Bush of Florida, and a brother of President Bush, had decided against entering the 2008 contest.

“If Jeb Bush were in, he would clear the field,” the GOP loyalist said. Among conservatives, Mr. Barbour’s name quickly emerged as a candidate who could appeal to the party’s base while also projecting charisma.

While he served as the national GOP chairman from 1993 to 1997, Mr. Barbour was a regular presence on network television. He delivered the party’s message with a jocular charm that often disarmed critics.

“He’s got tremendous media skills. He’s just very smooth,” a conservative activist in the capital said.

After winning the Mississippi governor’s job in 2003, Mr. Barbour made tort reform his leading priority. Last June, he signed a legal reform package that is likely to bring an end to the state’s reputation as a magnet for questionable tort cases and large jury verdicts.

While Mr. Barbour does not have strong ties to New York, Governor Pataki and Mayor Bloomberg held fundraisers for him in 2003. Mr.Barbour also made a visit to the city last year, touting the tort reform legislation and seeking investment for his home state.

Some New York Republicans say the native of Yazoo City, Miss., deserves serious consideration as a presidential contender.

“Does he have the ability and the credentials? Yes. He’d be a worthy candidate,” a Manhattan GOP fund-raiser, Lewis Eisenberg, said. “This country has some recent history where governors of a small southern state can ascend to the presidency.”

Mr. Eisenberg hastened to add that he has not yet decided whom to back in the 2008 race. He said Mr. Pataki, Mayor Giuliani, the governor of Massachusetts Mitt Romney, Senator McCain of Arizona, and Senator Frist of Tennessee are all serious contenders for the nomination.

Mr. Eisenberg said Mr. Barbour has earned a place on that list because of his successful leadership of the GOP in the 1990s. Mr. Barbour also served for two years as a political director for President Reagan. “He’d be a very strong player on a deep bench,” Mr. Eisenberg said.

Senator Lott of Mississippi is among those who think a Barbour candidacy is at least plausible. Last week, he told a Washington newspaper, the Hill, that Mr. Barbour or Mr. Romney would stand a better chance of winning the presidency than the senators who are widely mentioned as possible candidates. “I don’t think any senator can win the nomination,” Mr. Lott said.

Another Republican insider said the burden of serving and running at the same time will be particularly hard for Mr. Frist, the Senate majority leader. “There’s just still too many nicks and cuts, too many distractions, too many other battles,” the GOP loyalist said. “It’s going to be very difficult for Frist.”

Some political pundits dismissed the idea of a Barbour presidency as downright zany.

“It’s not a million-to-one shot. I think he’s a billion-to-one shot,” a prominent political analyst in Washington, Stuart Rothenberg of the Rothenberg Political Report, said.

But Mr. Rothenberg said he understands the appeal of Mr. Barbour in some quarters. “The one great asset he has is he can talk the good ol’ boy talk and also talk to the business/banker types,” Mr. Rothenberg said.

However, the newsletter publisher said Mr. Barbour’s Mississippi roots would ultimately prove more of a liability than a strength with voters across America. “It may not be altogether fair, but when they think of Mississippi, they think of the Old South, not the New South,” Mr. Rothenberg said. He said most voters still equate the state with low educational achievement and racial strife.

Some analysts have also expressed doubts about whether Mr. Barbour’s Southern charm would win converts in New Hampshire and Iowa, the states whose early contests often wield great influence over presidential races.

“The only reason people find him compelling is they’re realizing there’s a great chance this field will not have a superstar in it,” said Chuck Todd, the editor in chief of a daily tip sheet for political insiders, the Hotline. Mr. Todd said there is a significant chance that Mr. Giuliani and Mr. McCain may choose not to run in 2008, leaving the field to a group of people relatively unknown outside Washington and their home states.

“Suddenly, Haley Barbour and Newt Gingrich look interesting to people, but I think it’s by comparison,” Mr. Todd said, tossing in the name of a former House speaker who is now being discussed as a possible presidential candidate.

However, Mr. Todd said Mr. Barbour’s history as a Washington lobbyist would render him essentially unelectable as president. “The minute he takes this seriously, he’s got a million things he needs to answer for in lobbying contracts,” Mr. Todd said.

Some proponents of Mr. Barbour’s possible candidacy said he could run as a Washington outsider, but Mr. Todd said such an assertion would be laughable for a man whose lobbying firm, Barbour Griffith & Rogers, was dubbed the most powerful in the nation’s capital by Fortune magazine.

Mr. Barbour’s former clients include the tobacco industry and foreign countries such as Mexico. “That’s an obstacle and not a small obstacle,” Mr. Todd said. “It would keep reporters busy a long time.”

Mr. Barbour’s friends point out that all those arguments were raised against him in the Mississippi governor’s race, to no avail. Still, they acknowledge the scrutiny of the presidential race would be tougher.

“The firm is going to get raked over the coals,” one of those backing a Barbour bid said. “I think he would sail through it.”