The two will focus on national security issues in the important Southern state.
"They want a commander-in-chief that will have a steady hand and have a backbone and will support the troops and has detailed plans on how to keep us safe as it relates to Islamic terrorism," Jeb Bush said Wednesday on CNN's "New Day." "Here in South Carolina particularly that's an important issue."
George W. Bush won the South Carolina primary in his 2000 presidential race.
Jeb Bush headed to Hilton Head after placing fourth in the New Hampshire primary. Bush outperformed polls in the Granite State
, earning 11% support.
Bush said he can resonate with South Carolina voters -- who vote on February 20 -- more strongly than Donald Trump despite the Republican front-runner capturing about 35% of the New Hampshire vote.
"There's two-thirds of the Republican voters that didn't support him. And a lot of people won't support him because he insults people, he disparages people, he divides people," he said. "My case has to be, 'Look, I understand why you're angry. Here's the solution.'"
"I have an agenda that will be the antidote to the angst that people feel," Bush added. "Trump's a master at capturing people's angst, but he hasn't offered a compelling alternative to where we are right now."
Ohio Gov. John Kasich came in second in New Hampshire, but Bush said he doubts his rival will do as well in South Carolina.
"He has nothing going on down here. He has no tangible support," he said. "He's been a capable governor for sure. I'm the most conservative capable governor in the field here in South Carolina. They generally support the most conservative candidate that can win. I think that's me."