Speaking at a campaign fund-raiser before about 100 people at the Buckhead Club, Mr. Walker — who spent the day on a three-city swing through South Carolina — said the March 1 primaries through much of the South would be key to his chances of winning the nomination.

“We didn’t just come here by accident,” Mr. Walker said. “With March 1 being not long after those first four states, we think that the March 1 primaries — the S.E.C. primaries, if you will — are going to be incredibly important, and we feel we can do well.”

“Georgia’s going to make a difference,” he added, “so get used to seeing us.”