How a campaign raises money matters. Because of strict campaign contribution limits of $3,300 per person for the primary, campaigns that raise money chiefly from bigger contributors cannot return to those same donors again and again for support.

Small contributors are particularly valuable because they can give $30 more than 100 times before bumping up against contribution caps.

Tim Tagaris, a Democratic digital strategist who oversaw the Sanders fund-raising operation in 2020, called the number of DeSantis donors surprisingly small.

Mr. Tagaris said that 40,000 “donations in a week for a leading presidential campaign is either a sign that they didn’t prepare well enough heading into the launch or there isn’t the kind of grass-roots support from regular people they had probably hoped for.” He added, “That’s a donor number you expect from top-tier Senate campaigns, not a leading presidential.”

But Eric Wilson, who has worked as a Republican digital strategist, called the number of donors a “good start” for a candidate who had not previously sought federal office.

“That is what someone needs to take on Trump, because he obviously had one of the best donor files,” said Mr. Wilson, who is now the director of the Center for Campaign Innovation, a conservative nonprofit.

One previous presidential candidate with a similar starting number of total donors was Kamala Harris, who had 38,000 in her first day in 2019. She raised $1.5 million that day — which indicates just how many bigger checks Mr. DeSantis received.

Mr. Wilson cautioned against comparing Republican and Democratic campaigns because Republican donors are more than a decade behind on “building an online grass-roots donor culture.”

The DeSantis campaign did not immediately respond to a request for comment.

The $8.2 million opening total that Mr. DeSantis has claimed remains impressive. It exceeded the Sanders figure and broke the kickoff record set by President Biden in his 2020 campaign.

It is not clear what portion of the $8.2 million is from funds earmarked for the general election. The campaign has said it was collecting up to $3,300 in general election contributions, which Mr. DeSantis can’t spend during the primary and would have to return if he doesn’t win the nomination.

Overall, money is expected to be a DeSantis strength, especially because his allied super PAC has said it expects to have at least a $200 million budget.

But online funds have become increasingly scarce for Republicans since last summer, including for Mr. Trump — until his recent indictment at least temporarily turbocharged his fund-raising.

The 40,000 donors that Mr. DeSantis had in his first week also happens to be the threshold that the Republican National Committee just set for candidates to qualify for the first debate stage.

That figure was never expected to be a problem for Mr. DeSantis. But the fact that the candidate polling second to former President Donald J. Trump in almost every poll hit that mark during his kickoff week is a sign of just how onerous that figure is likely to be for smaller campaigns.

The DeSantis team made no secret that it was soliciting big money to coincide with his kickoff. The campaign had gathered major donors at the Four Seasons in Miami for an event they called Ron-O-Rama. Officials in the DeSantis administration were also soliciting donations from Florida lobbyists, which gave some the impression that the governor’s office was tracking their donations at a time when the state budget — and Mr. DeSantis’s veto pen — hung in the balance.