Lt. Gov. Casey Cagle downplayed his chances of winning Tuesday's primary outright and said his campaign was quietly preparing for a likely runoff against Secretary of State Brian Kemp or former state Sen. Hunter Hill.

As he embarked on an eight-stop flyaround Monday to the state's largest media markets, Cagle said it would be "very challenging" to emerge with the majority-vote needed to avoid a July 24 runoff against the runner-up.

“That’s a very high hurdle to overcome. But we’re very excited about where we are. We’re clearly in a very good position going into Election Day,” he said. “And obviously we’re very prepared for a runoff and have already begun that process.”

The debates were held at Channel 2's studios.

Public polling shows the two Republicans jockeying for the No. 2 spot in Tuesday’s crowded race, with executive Clay Tippins and state Sen. Michael Williams trailing. The surveys have showed Cagle with a consistent lead, putting him either in the 30s or low-40s.

The lieutenant governor also urged his potential future opponent to steer clear of "nasty" rhetoric that could weaken the eventual GOP nominee in a high-profile November campaign against one of two Democrats – former House Minority Leader Stacey Abrams or ex-state Rep. Stacey Evans - battling for the nomination.

“Hopefully, we can avoid that, and everyone can commit to talking about the issues and running a positive campaign, talking about the vision they have for the state,” he said. “We’re the only candidate that has cast a very clear vision of substantive public policy issues versus gimmicks, hot air and false attacks.”

At a nearby stop before his own air tour, Kemp said Cagle’s recent attacks - he swung at Hill repeatedly in Sunday’s debate - show he’s getting nervous.

“Casey Cagle is going after everyone, and it shows he’s a desperate politician, quite honestly, that’s losing his almost quarter-century grasp of going to the Capitol to work every day,” said Kemp.

All five GOP candidates have raced to the party's flanks, trying to outdo each other with aggressive promises on a blend of tried-and-true conservative issues such as cutting taxes and cracking down on illegal immigration.

Cagle has picked a fight with Decatur over immigration policy, joined his GOP rivals in supporting "constitutional carry" gun rights and pledged to send Georgia National Guard soldiers to the Mexican border to fight illegal immigration.

But he hasn’t gone as far as some of his rivals on some of those issues. He’s offered more modest tax-cut plans than Hill, while he wouldn’t match Kemp’s calls to pass the nation’s toughest abortion restrictions.

Read more: Big changes in Georgia politics at stake in Tuesday's vote 

Read more: Understanding Georgia's race for governor