Republican Gov. Chris Sununu of New Hampshire says, "I hate this woke cancel culture stuff."

But the popular longtime governor of a key northeastern battleground state who describes himself as a "free market-principled conservative" says he disagrees with Republican Gov. Ron DeSantis’ culture wars strategy of targeting corporations over woke policy.

"I think the best foundation of the Republican Party is limited government, local control. Appreciating that private businesses and the free market are what made this country great," Sununu said in an interview with Fox News Digital on Friday during a major GOP donor conference hosted by the politically influential, fiscally conservative group Club for Growth.

The disagreement about how to handle "woke" corporations may ultimately play out on the 2024 presidential campaign trail if both young governors, who are rising stars in the party, move ahead and launch White House runs. 

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DeSantis in Palm Beach

Florida Gov. Ron DeSantis speaks as he announces a proposal for Digital Bill of Rights, Wednesday, Feb. 15, 2023, at Palm Beach Atlantic University in West Palm Beach, Fla.  (AP Photo/Wilfredo Lee.)

Florida's governor, a former congressman, saw his popularity soar among conservatives across the country over the past three years due to his forceful pushback against coronavirus pandemic restrictions and his aggressive actions as a conservative culture warrior going after media, corporations and teachers unions.

In his speech Thursday night kicking off the three-day confab, DeSantis hit back at some potential rivals for the GOP presidential nomination, who have criticized his aggressive actions in going after "woke" corporations, particularly his battle against Disney.

"Some people who claim to be on the right have said we somehow were interfering with the free market with what we did with Disney," DeSantis said.

Pointing to a bill he signed into law on Monday that limits Disney’s autonomy in Florida, DeSantis argued, "I think we’ve brought some equilibrium to this."

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"I don’t think it works if you say corporate America can advance the Left’s agenda with no check and balance if we’re just going to act like it’s none of our business, because it’s affecting our county, and if woke ideology takes over it will destroy this country. We are not going to let that happen in the state of Florida," the governor said.

DeSantis insisted that "Republicans need to not shy away from these fights just because the media and the Left’s going to call you names."

"Some of these Republicans, they just sit back like potted plants, and they let the media define the terms of the debate. They let the Left define the terms of the debate. They take all this incoming, because they’re not making anything happen," he claimed.

Republican Gov. Chris Sununu of New Hampshire speaks at a donor conference hosted by the conservative group the Club for Growth, on March 3, 2023, in Palm Beach, Florida

Republican Gov. Chris Sununu of New Hampshire speaks at a donor conference hosted by the conservative group the Club for Growth, on March 3, 2023, in Palm Beach, Florida (Fox News )

But Sununu argued that "[going] after someone because they politically disagree with you, that ain’t what were about. That’s not what Republicans are about. That’s not what America’s about." Referring to DeSantis, he said, "He’s got a lot of headlines off of it, and I understand that. We’ve got two very different styles," Sununu added.

Sununu reiterated that "I hate this woke cancel culture stuff. It’s a disaster. But government doesn’t solve a cultural problem. That’s what Democrats try to do. Big government will solve your cultural problem. No, no, no, no, no. That’s not what Republicans are about. We solve it community to community, person to person, school to school. I would say we politely differ in that respect."

When it comes to defeating wokeness in big business, New Hampshire’s governor predicted that "the free market will take care of it"

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Similar to DeSantis, Sununu is currently dealing with this state’s legislative session, and any 2024 announcement likely would come following the conclusion of that session and the signing of the state’s next biennial budget.

"I think the entire presidential timetable will start coming into full vision, full gear, later this summer sometime. We’re not rushing anything. There’s a lot of interest and that’s kind of exciting," Sununu told Fox News. 

Pointing to the first two contests in the GOP presidential nominating calendar, the governor noted that "you’re talking about states like Iowa and New Hampshire, where the vast majority of people don’t make their decision until the last few weeks. There’s lots of opportunities. The average voter is just getting over the hangover of November of '22."

Sununu said, "Our organization’s really about making the party bigger, talking to independents, talking to the next generation of voters. That’s going very, very well. We’re doing a lot of earned media all across. We’re having some fun and bragging about the New Hampshire model."

The governor, who’s become a vocal Donald Trump critic in recent years, called the former president's White House run "the orange-haired elephant in the room" in a speech Friday to the donors gathered at the Club retreat.

Former President Donald Trump

Former President Donald Trump speaks at a campaign event at the South Carolina Statehouse, Jan. 28, 2023, in Columbia, South Carolina. (AP Photo/Alex Brandon, File)

"I supported Trump in ‘16, I supported him in ’20. I think he did some very good stuff. But thank you very much, we’re moving on. Unfortunately, there’s a lot of independents that were with us and just stepped to the side and said, 'No, if that’s your flag bearer, I’m not going to be there.’ I think most folks agree, we’ve got to move on if you want to win in ’24," Sununu said.

Sununu argued that when it comes to the 2024 general election, "there’s no avenue for him [Trump] to win."

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But he also stressed that Republicans need to "be inspirational in terms of our leadership. Let’s be aspirational. Let’s make sure we are the team folks want to join and that we’re leading with that type of message."

He criticized the GOP, charging that "our messaging is frankly so bad at times, we step all over ourselves. . . . We let the Democrats define us." 

As for his own efforts, Sununu told Fox News: "We’re raising money into our organization. We have a 501c4 called Live Free or Die. It’s allowing us to go out and talk about that model of success, talk about making the party bigger. Talk about getting people excited, about being on the team."