Mr. Bloomberg, a frequent guest on “The Daily Show,” also recognized Mr. Stewart’s role.

“Success always has a thousand fathers,” the mayor said in an e-mail. “But Jon shining such a big, bright spotlight on Washington’s potentially tragic failure to put aside differences and get this done for America was, without a doubt, one of the biggest factors that led to the final agreement.”

Though he might prefer a description like “advocacy satire,” what Mr. Stewart engaged in that night — and on earlier occasions when he campaigned openly for passage of the bill — usually goes by the name “advocacy journalism.”

There have been other instances when an advocate on a television show turned around public policy almost immediately by concerted focus on an issue — but not recently, and in much different circumstances.

“The two that come instantly to mind are Murrow and Cronkite,” said Robert J. Thompson, a professor of television at Syracuse University.