WASHINGTON (CNN) -- South Carolina Republican Party Chairman Katon Dawson advised fence-sitting candidates Tuesday to fire up their campaign machines now or risk missing the narrowing window to jump into the presidential contest.

"This process will be over this time next year, and there's only a couple of weeks left for people to get in and put organizations on the ground, finance teams in place and media teams in place," Dawson said in an interview with CNN Senior Political Analyst Bill Schneider. "And again, my advice would be to get on the ball and get in the race if you're interested in being President of the United States, whether it be Democrat or Republican."

Some high-profile Republicans including former Sen. Fred Thompson of Tennessee and former House Speaker Newt Gingrich of Georgia have acknowledged they are seriously considering White House bids. Gingrich has been voicing interest for months, while Thompson has only recently said he is considering a presidential bid.

"I've certainly seen a lot of excitement for Sen. Thompson," Dawson said. "We know him. We've watched his record in Washington, and I think that he'd be a very viable candidate in a large field of Republicans that all bring something different to the process."

And despite the intense campaigning in his state by the Republican presidential hopefuls, Dawson said there is no "natural frontrunner right now."

-- CNN Political Editor Mark Preston