Many rank-and-file Republicans and party leaders say yes, as the 61-year-old Barbour prepares to ramp up his national profile this month with back-to-back trips to the early presidential voting states of Iowa and New Hampshire.
Barbour will headline fundraisers in both states, but says the visits are part of his duties as incoming chairman of the Republican Governors Association. Both states have governors' races next year.
"I've told everyone I know that every Republican ought to be focused on governors' races in 2009 and the 2010 elections," Barbour said in an interview with The Associated Press.
A former chairman of the Republican National Committee, Barbour has emerged as a leader of his party's efforts to retool for the future. His allies believe he could be a formidable presidential contender if he chooses to play.
"Haley's unique in that he's a brilliant strategist who led the party and has also run in and won a competitive governor's race," said Ed Gillespie, a former RNC chairman. "He commands a lot of respect from rank-and-file Republicans, as well as the leadership of the party and many Democrats. He's a happy warrior who stands up for conservative principles."
Barbour typically sidesteps questions about his presidential aspirations, saying he will wait until after next year's elections to decide.
With his good ol' boy charm and a drawl as thick as Mississippi mud, Barbour at first blush might not fit anyone's idea of the standard bearer for a party looking to diversify. He's a former lobbyist who made millions representing tobacco and other business interests, even as lobbyists increasingly have become stigmatized by Democrats and Republicans alike.
But Barbour's political skills have been tested and proven in Mississippi, where he defeated a Democratic incumbent to become just the second Republican elected governor since Reconstruction, and at the national level, where he helped rescue the GOP during another low period for the party.
Barbour became RNC chairman in 1993 after Bill Clinton was elected president and Democrats held strong majorities in Congress. Led by Barbour and Newt Gingrich, another potential 2012 contender, Republicans rallied in 1994, claiming majorities in the Senate and in the House for the first time in 40 years.
The Republican gains that year were helped by the collapse of the President Bill Clinton's health care reform plan; President Barack Obama is making a politically risky attempt to reform the nation's health care system this year, with potential reverberations in next year's midterm elections.
Barbour left the RNC in 1997 and built a lucrative lobbying practice before returning to Mississippi to run for governor. He defeated Democrat Ronnie Musgrove in 2003 and was easily re-elected in 2007; term limits will require him to step down after 2011.
Barbour has governed as a conservative, which is sure to endure him with Republicans across the country. But coming from a state in the heart of the old Confederacy that hasn't voted for a Democratic presidential candidate since 1976, his appeal to independents and Democrats is open to question.
Barbour cut Medicaid costs by imposing renewal rules that led to thousands of people being dropped from the rolls. But he also signed into law this year a major cigarette tax increase, raising the rate from 18 cents a pack to 68 cents.
From the beginning, Barbour pushed legislators to trim the state budget by closing some state parks and cutting other expenses. While he claims credit for having fixed the budget problems "without raising anybody's taxes," local officials complained that they were forced to increase taxes because some state expenses were forced down on them.
Barbour has been a sharp critic of federal stimulus spending this year along with other a few other GOP governors, including Mark Sanford of South Carolina, Bobby Jindal of Louisiana and Sarah Palin of Alaska. All are considered possible 2012 presidential contenders.
Barbour has rejected some $56 million in federal stimulus money for unemployment compensation, saying he objected to the requirement that Mississippi extend unemployment benefits to people seeking part-time jobs.
Barbour's first term as governor was shaped by Hurricane Katrina, which left a wide swath of destruction across his state in August 2005. His response to the storm was widely praised even as Kathleen Blanco, Louisiana's Democratic governor at the time, was panned for botching recovery efforts there.
But many Democrats argued that Barbour's job was made easier by friends in high places.
Mississippi's senior senator, Republican Thad Cochran, was chairman of the Senate Appropriations Committee when Katrina struck, and he helped steer billions of dollars to his home state. And officials in Louisiana said that as Republicans, Barbour and Cochran received unfair preferential treatment by the Bush administration in coping with the storm's aftermath.
Other critics, including the Mississippi chapter of the National Association for the Advancement of Colored People, complained when Barbour won approval from the federal government in 2008 for his plan to divert $570 million from a $5.4 billion grant from a hurricane-recovery housing program and expand the state port.
Steve Holland, a Democratic legislator in Mississippi who has clashed repeatedly with Barbour, commended the governor's smooth handling of Katrina recovery, but said it was little more than a distraction from Barbour's overall record of opposition to social spending.
"You have to be a totally devoted far-right, conservative person to appreciate his zeal and zest for unbridling the government," Holland said. "He's always against every damn thing you bring up, especially quality of life issues, people issues, hard issues. He's one of the most cold-hearted human beings I've ever met."
Barbour's friends differ, calling him a personable, gifted politician who would make a strong candidate and good president. His biggest problem, they say, is the accident of timing - despite his skills, would the party nominate a white, Southern former lobbyist to challenge the first black president?
"Haley is born to the job from a policy, intellectual and political standpoint," said Ed Rogers, Barbour's former lobbying partner. "He can go deep on issues and sincerely loves people. It would be fun for him to go to the pancake breakfasts in every county in Iowa."