Liberals across the country are looking to Bill de Blasio, who was sworn in as mayor early Wednesday, to morph New York City’s municipal machinery into a closely watched laboratory for populist theories of government that have never before been enacted on such a large scale.

The elevation of an assertive, tax-the-rich liberal to the nation’s most prominent municipal office has fanned hopes that hot-button causes like universal prekindergarten and low-wage worker benefits — versions of which have been passed in smaller cities — could be aided by the imprimatur of being proved workable in New York.

“The mayor has a remarkable opportunity to make real many progressive policies and prove their merit,” said Gavin Newsom, the lieutenant governor of California, who as mayor of San Francisco introduced a form of universal health care and allowed same-sex couples to wed.

“De Blasio matters,” Mr. Newsom said. “A lot of us are counting on his success.”

New York has long been a lodestar for urban governments the world over. The avant-garde policing pioneered by former Mayor Rudolph W. Giuliani transformed the way major municipalities fight crime. Mayor Michael R. Bloomberg’s corporate-minded approach to education and feats of social engineering, like the ban on smoking in bars, quickly gained global traction.