Mayor Jim Kenney was elected in Philadelphia last year after promising to bring the city universal prekindergarten, but he needed a way to pay for it.

Enter the soda tax. As part of his budget, introduced this month, Mr. Kenney has proposed taxing sugar-sweetened beverages at 3 cents an ounce, the highest soda tax proposed anywhere in the country.

The idea of a soda tax was introduced about a decade ago by public health researchers who were aiming to reduce consumption of sugary drinks, which they argued were causing increases in obesity and diabetes. But the message has been a tough political sell. Soda tax proposals, fought by the soda industry as nanny-state excess, have failed in New York State, San Francisco — and Philadelphia, twice. So far, the only American city to pass a soda tax is Berkeley, Calif.

Mr. Kenney is taking a different political tack. Instead of the usual eat-your-vegetables pitch of public health reformers, he is offering Philadelphians something delicious: a giant pot of money to fund popular city projects. He says his soda tax could raise more than $400 million over five years, enough to fund not just universal preschool, but also renovations to local libraries, parks and recreation centers; “community schools” that wrap social services with education; and cash for the troubled municipal pension program. He is not using the word obesity, or suggesting that people should drink less soda.