Mr. DeSantis’s announcement had been an opportunity for Mr. Musk, an unpredictable executive with interests in many fields, to promote his multiple agendas. Those included a political coming-out for the billionaire, who has flirted with right-wing accounts and politics for years on Twitter but has never embraced a presidential candidate the way he has the Republican governor. And it was supposed to be a way for Mr. Musk to advance his business interests by highlighting Twitter, which he is trying to turn around.

Yet as the Twitter audio livestream faltered, the reaction — including on Twitter itself — was shock and scorn that what should have been a carefully choreographed announcement of a presidential run had stumbled so badly. The hashtag #Desaster appeared on many posts. Others took potshots at the failure, with President Biden’s personal @JoeBiden account tweeting a donation link with the words, “This link works.”

David Sacks, a tech executive who moderated the audio event with Mr. DeSantis and who is a confidant of Mr. Musk’s, tried downplaying the technical problems.

“We got so many people here that we are kind of melting the servers, which is a good sign,” he said during the first livestream, which sputtered out.

Mr. Musk did not respond to a request for comment.

Inside Twitter, employees had been alarmed by Mr. Musk’s turn into politics and whether the social media site could handle the influx of traffic, three employees said. There was no planning for what are known as “site reliability issues” for the event with Mr. DeSantis, two of the people said, and workers were prepared to do whatever they could to keep the social network running.