Still, some have expressed doubts that start-ups can change the trajectory of a state whose economic output is about the same as it was in 2005.

“The Lamonts are talking about innovation, but if, say, we get start-up companies here and they grow at a rate of 60 percent a year, that’s too slow,” said Fred Carstensen, director of the Connecticut Center for Economic Analysis at the University of Connecticut.

“In terms of scale, what you really want to do is get a Pratt & Whitney to put a facility with 1,500 jobs here,” Mr. Carstensen added. “What Connecticut really needs is big hits.”

Mr. Lamont, 65, started a cable television company in the 1980s, but he is better known for his political campaigns. In 2006, he beat three-term incumbent Joe Lieberman in the Democratic primary for Senate, but lost to Mr. Lieberman, who ran as an independent, in the general election. He sought the Democratic nomination for governor in 2010, but lost to Dannel P. Malloy, the outgoing governor.

Mr. Lamont, whose great-grandfather was a business partner of J.P. Morgan, spent $38 million of his own money on his campaigns, including $12 million to win the governor’s race in November.

Now he inherits a state striving to reverse its financial fortunes.

General Electric dealt the state a particularly harsh blow when it announced in 2016 that it was moving its headquarters to Boston in search of a deeper pool of high-tech workers. When Mr. Lamont learned the news, he called a Yale classmate and neighbor in Greenwich, Indra Nooyi, who was the chief executive of PepsiCo.