After his unusual, buzzy and ill-fated presidential debut on Twitter last week, Gov. Ron DeSantis of Florida carried out a far more traditional campaign tour this week, barnstorming Iowa, New Hampshire and South Carolina to sell himself as the strongest Republican alternative to former President Donald J. Trump.

Along the way, he drew sizable, enthusiastic crowds of DeSantis-curious voters. He held babies. He got testy with a reporter. He threw some punches at Mr. Trump. He warned of a “malignant ideology” being pressed by liberals and vowed to “impose our will” to stop it.

Here are five takeaways.

For months, Mr. DeSantis held his fire against Mr. Trump. Those days are clearly over.

“Petty,” he labeled Mr. Trump’s taunts. “Juvenile.” The former president’s criticisms of him? “Bizarre” and “ridiculous.”

But Mr. DeSantis made those remarks not from the stage, in front of Republican voters, but behind the scenes in comments to reporters, suggesting that he is not quite ready to attack Mr. Trump head-on. Instead, his most direct shots were saved for President Biden (“We’re going to take all that Biden nonsense and rip it out by the roots”).

When it comes to Mr. Trump, the governor has said he is simply defending himself from a man with whom he avoided public disagreements for years.

“Well, now he’s attacking me,” a seemingly aggrieved Mr. DeSantis said outside Des Moines.

There are risks to bashing Mr. Trump. For some voters, part of Mr. DeSantis’s appeal has been his willingness to avoid warring with a fellow Republican.

“DeSantis has Trump policies, without all the name-calling,” said Monica Schieb, an Iowa voter who supported Mr. Trump in 2016 but now plans to back Mr. DeSantis.

Mr. DeSantis packed his schedule with three or four rallies per day, covering hundreds of miles in each state and addressing a total of more than 7,000 people, his campaign said.

The events did not quite have the MAGA-Woodstock energy of Mr. Trump’s arena rallies, but they were lively and well-attended. Tightly orchestrated, too: There was no chowing of hoagies or cozying up to bikers at diners. Up-tempo country music and occasionally cheesy rock (“Chicken Fried” by the Zac Brown Band and “Eye of the Tiger” by Survivor) preceded him onstage.

The message behind the rigorous schedule?

Turning the country into a mega-Florida takes a “disciplined, energetic president,” in his words.

It’s a phrase we’re likely to hear more of, given that it takes aim at both of the major obstacles in Mr. DeSantis’s path to the White House: Mr. Trump and President Biden.

At nearly every event, Mr. DeSantis, 44, used comments about his energy level as an indirect swipe at his much older opponents. Mr. Trump is 76; Mr. Biden is 80. And Mr. DeSantis regularly noted that unlike his main Republican rival, Mr. Trump, he would be able to serve two terms.

The messaging allowed Mr. DeSantis to set a clear contrast with the former president without necessarily angering Mr. Trump’s loyal supporters.

Two terms, the governor says, would give him more time to appoint conservative Supreme Court justices and unwind the “deep state.” (Mr. Trump responded angrily to the new line of attack, saying in Iowa on Thursday that “you don’t need eight years, you need six months,” adding, “Who the hell wants to wait eight years?”)

The case Mr. DeSantis is making, however, sometimes seems to be undercut by his own delivery. Even supporters acknowledge that he is not a natural orator, and on the stump he sometimes calls himself an “energetic executive” in a neutral monotone.

If Mr. DeSantis had to summarize what he believes is wrong with America in one word, his three-state tour suggests the answer might be “woke,” a term that many Republican politicians find easy to use but hard to define. The governor frequently rails against “wokeness,” which he describes as a “war on the truth,” in distinctly martial terms.

At several events, Mr. DeSantis, a military veteran, seemed to borrow from Winston Churchill’s famous “We shall fight on the beaches” speech, given to exhort the citizens of Britain in their existential struggle against Nazi Germany.

“We will fight the woke in education,” Mr. DeSantis said in New Hampshire. “We will fight the woke in corporations. And we will fight the woke in the halls of Congress. We will never surrender to the woke mob.”

(Mr. Trump seemed to take a shot at his rival’s use of the word, saying on Thursday, “I don’t like the term ‘woke,’ because I hear ‘woke, woke, woke.’” He added: “It’s just a term they use. Half the people can’t even define it. They don’t know what it is.”)

Earlier, at his kickoff rally outside Des Moines on Tuesday night, Mr. DeSantis seemed to put the various building blocks of his stump speech together into a coherent vision, one that portrayed the United States as a nation being assaulted from the inside by unseen liberal forces bent on reshaping every aspect of American life.

“They are imposing their agenda on us, via the federal government, via corporate America, via our own education system,” he said. “All for their benefit and all to our detriment.”

In turn, Mr. DeSantis promised to aggressively wield the power of the presidency in order to resculpt the nation according to conservative principles, much as he says he has done in Florida, where he has often pushed the boundaries of executive office.

“It does not have to be this way,” he continued in his Iowa kickoff speech. “We must choose a path that will lead to a revival of American greatness.” The line drew cheers.

Both detractors and supporters were watching closely for how Mr. DeSantis, who sometimes appears uncomfortable with the basics of retail politics, interacted with voters. Democrats and Trump allies have made a legion of memes out of his uncomfortable facial expressions or clumsy responses to voters in casual conversations. (An emphatic “OK!” is often his answer to learning a person’s name or a child’s age.)

But apart from a pugnacious exchange or two with the news media — episodes that are, of course, cheered by the Republican base — Mr. DeSantis avoided obvious awkward moments. He tried to make himself relatable, playing up his dad credentials. He told stories about taking his family out for fast food and contending with a 3-year-old who needed to use the “little potty.”

After his speeches, he worked the rope line, talked with voters, snapped pictures and signed autographs. He always reacted enthusiastically when voters told him they lived part-time in Florida. “What part?” was his standard follow-up, before discussing how badly those areas had been hit by Hurricane Ian.

While this all might be a low bar, it was set, in part, by Mr. Trump’s relentless mockery of Mr. DeSantis’s personality.

Frank Ehrenberger, 73, a retired engineer who attended a DeSantis event in Iowa on Wednesday, said the governor had struck him as “genuine.”

Still, Mr. DeSantis may need to do more. At events in Iowa and New Hampshire on Wednesday and Thursday, he did not take audience questions from the stage, leading to some criticism. Instead, at one stop in New Hampshire, Mr. DeSantis tossed baseball caps to the crowd.

The early nominating states require a set of political skills different from the one that works in Florida, where politicians rely heavily on television advertising to get their messages across.

By Friday, during his visit to South Carolina, he had seemed to shift his strategy, electing to answer voters’ questions from the stage alongside his wife, Casey DeSantis.

At his events, Mr. DeSantis has paused his stump speech to invite Ms. DeSantis onto the stage to deliver her own remarks. As she speaks, he usually stands smiling behind her before returning to the lectern to close out his speech. At one stop in New Hampshire, he kissed her temple after she had finished.

These intermissions — not unprecedented, but unusual as a routine at presidential campaign events — underscore the high-profile role Ms. DeSantis is expected to play her in husband’s bid, after acting as an important adviser in his political rise.

If this first tour is anything to go by, she is likely to be one of the most prominent and politically active spouses of a major presidential candidate in several election cycles, perhaps since Bill Clinton in 2008.

Onstage, Ms. DeSantis tells the usual marital stories meant to humanize candidates and illustrate their family life — including an oft-repeated bit about the time one of their three children wielded permanent markers to decorate the dining room table in the governor’s mansion.

But she is far from light entertainment. Much of her roughly five-minute speech is meant to portray her husband, whom she often refers to as “the governor,” as an authoritative, decisive leader, one capable of cleaning up “the swamp” in Washington.

“Through all of the history, all the attacks from the corporate media and the left, he never changes,” Ms. DeSantis said Thursday in New Hampshire. “He never backs down, he never cowers. He never takes the path of least resistance.”

Ann Klein contributed reporting from Cedar Rapids, Iowa, and Bret Hayworth from Salix, Iowa.