NEW YORK (AP) — In his first week on the campaign trail as a presidential candidate, Florida Governor Ron DeSantis repeatedly hit his chief rival, Donald Trump, from the right.

“This is a different guy than 2015, 2016,” DeSantis told a conservative radio host before slamming the bipartisan criminal justice reform legislation Trump championed as “basically a jailbreak bill” that allowed dangerous people out of prison.

He also accused Trump of “turning the reins over” to Dr Anthony Fauci during the COVID-19 pandemic, said Trump had “ endorsed and tried to ram” an “amnesty” bill through Congress and vowed that — unlike the former president — he would finish building the US-Mexico border wall.

In Iowa on Saturday, he hit back at Trump for saying he didn’t like the term “woke” because people have a hard time defining it. “Woke is an existential threat to our society,” DeSantis said. “To say it’s not a big deal, that just shows you don’t understand what a lot of these issues are right now.”

Trump, meanwhile, has repeatedly attacked DeSantis from the left. He has suggested that even anti-abortion activists consider Florida’s new six-week abortion ban “too harsh” and argued that DeSantis has made himself unelectable on a national level with his votes as a congressman to cut Social Security and Medicare — even though Trump’s proposed budgets also repeatedly called for major entitlement cuts.

The attacks underscore the underlying early dynamic of the race: As DeSantis tries to win over GOP primary voters and chip away at Trump’s commanding early lead, Trump is already pivoting to a general election matchup against President Joe Biden. In the meantime, Trump has been pushing back against DeSantis’ argument that the Florida governor, not the former president, is the more viable general election candidate.

“Don’t forget, we have to win elections,” Trump stressed during a Fox News Channel town hall on Thursday as he discussed abortion politics.

To be clear, Trump has also leaned in on other right-wing causes. This week, he revived his pledge to end birthright citizenship, saying he would sign an executive order on the first day of his second term to change the long-settled interpretation of the 14th Amendment. He also renewed his pledge to use the US military to attack foreign drug cartels and has pushed the death penalty for drug dealers.

But DeSantis’ efforts to out-Trump Trump have raised eyebrows among some observers who question his tactics.

“I do not think it’s a smart strategy,” said Sarah Longwell, an anti-Trump Republican political strategist whose firm has been leading weekly focus groups with GOP voters where DeSantis’ appeal has been fading.

Longwell said she had expected DeSantis to tailor his pitch to the slice of the Republican electorate that wants to move on from Trump.

“You can’t out-MAGA Trump,” she said, referring to Trump’s “Make America Great Again” political movement. DeSantis, she argued, should be working to “consolidate the ‘Move on from Trump’-ers and move into the ‘Maybe Trump’-ers, and instead he’s tried to wrestle Trump for the ‘Always Trump’-ers.”

DeSantis allies argue the governor has been responding to what they see as Trump’s attacks from the left and highlighting his stances on issues they believe will resonate with Republican primary voters, particularly abortion and DeSantis’ PR war with Disney.

An official from Never Back Down, a pro-DeSantis super PAC handling much of his political operation, said DeSantis’ strategy is being informed by what the group’s canvassers have been picking up from voters in recent weeks. The official, who spoke on the condition of anonymity to discuss messaging strategy, said voters have voiced confusion about Trump’s attacks and have responded especially well to portrayals of DeSantis as a fighter who refuses to back down.

The group ran a digital ad this week highlighting Trump’s comment on abortion that was geotargeted to areas Trump was visiting in Iowa. It is also exploring messaging that will accuse Trump of being too cozy with major corporations during his time in the White House.

Trump spokesperson Steven Cheung slammed DeSantis’ insinuations and accused him of ripping off Trump’s ideas.

“Ron DeSantis has tried to steal every single one of President Trump’s Agenda47 policy platform. He is a fraudster and masquerading as someone who knows what he’s talking about,” he said.

DeSantis, in his early campaign stops, has also tried to paint himself as a disciplined executive who will make good on his promises, implying Trump had not.

“When I tell you I’m going to do something, I don’t just say that because I think that may be what you want to hear, then get into office and forget all the promises I made,” he said in Lexington, South Carolina.

Longwell said her research had consistently found that on-the-fence voters are willing to put aside concerns about Trump’s temperament because they feel he was so effective in office, raising questions about DeSantis’ strategy.

“They don’t like his mouth, they don’t like his tweets, they don’t like his character. But they like what he did as president,” she said.

Trump, meanwhile, has made clear he is looking toward next year’s general election.

In Grimes, Iowa, on Thursday, Trump received a pointed question from a woman who claimed that “we have lost people because you supported the jab,” a reference to conspiracies about mRNA vaccines, which have been credited with saving millions of lives.

While Trump did not dismiss her suggestion — and stressed that he was never in favor of mandates — he explained that “there’s a big portion of the country that thinks that was a great thing, you understand that. Not a lot of the people in this room, but there is a big portion.”

During the Fox News town hall later that day, Trump said “only stupid people” could suggest they had done more than him on abortion given that he picked some of the conservative Supreme Court justices who overturned Roe v Wade. But he also continued to criticise conservative Republican midterm candidates who did not support exceptions, including when the life of the mother is at risk, a position in line with the majority of voters.

A recent memo to donors from Trump super PAC pollster Tony Fabrizio, first reported by Axios, made the case that DeSantis is vulnerable among swing state voters in a general election on issues including cuts to Social Security and Medicare, book bans in schools, Florida’s ban on abortions at six weeks — before most women know they are pregnant — and his fight with Disney.

Voters, meanwhile, have mixed views about the escalating feud.

Heidi Lillibridge, a 51-year-old farmer and Republican activist from Vinton, Iowa, worries that Democrats will benefit from the two leading GOP candidates criticising each other. She is particularly frustrated by DeSantis’ early attacks.

“Criticizing President Trump’s conservative credentials, when we all know how he acted as president and what he got accomplished, I don’t really know why he would do that,” she said.

Darcy Cowart, who saw DeSantis speak outside a bar and restaurant in Bluffton, South Carolina, said that while she had previously backed Trump, she was glad to see a large field with other options.

“He’s not going to change, and he just has this bully mentality. He just won’t give in on it,” she said. “I know he fights for us, and I know that he does some good things, but at the same time, it’s like having this obnoxious relative that’s always got to be at the dinner table, that you dread being around.”