Haley's homespun charm would do fine. People from the South have held national office many times. Check the current occupant of the White House.
But beyond mere accent, Haley is a genuine character, he's extremely shrewd and well-connected. He ran the RNC when the GOP took back the House. He is a nuts and bolts party guy who understand the machinery of national and local politics, and his rolodex is a mile long. Everyone in the GOP owes him a favor in come capacity.
Barbour handled Katrina in Giuliani-esque fashion, in sharp contrast to his neighbors in Louisiana, and was hit harder in most areas.
But any man who unwinds at the end of the day with a Maker's Mark on ice is my kind of guy.