Public radio and television broadcasters are girding for battle after the Trump administration proposed a drastic cutback that they have long dreaded: the defunding of the Corporation for Public Broadcasting.

The potential elimination of about $445 million in annual funding, which helps local TV and radio stations subscribe to NPR and Public Broadcasting Service programming, could be devastating for affiliates in smaller markets that already operate on a shoestring budget.

Patricia Harrison, the corporation’s president, warned in a statement on Thursday that the Trump budget proposal, if enacted, could cause “the collapse of the public media system itself.”

But the power players in public broadcasting — big-city staples like WNYC in New York City — would be well-equipped to weather any cuts. Major stations typically receive only a sliver of their annual budget from the federal government, thanks to listener contributions and corporate underwriters. Podcasts and other digital offshoots have also become significant sources of revenue.

Rural affiliates, however, rely more heavily on congressional largess, which can make up as much as 35 percent of their budgets. Mark Vogelzang, president of Maine Public, called the Trump proposal “the most serious threat to our federal funding” since he started in public broadcasting 37 years ago.

“We’re always living on the edge in this ecosystem of public broadcasting,” Mr. Vogelzang said in an interview.

The Corporation for Public Broadcasting supports about 1,500 stations that carry a range of educational, journalistic and arts-related programming. The corporation dates to the administration of President Lyndon Johnson. Its funding, while a minuscule part of the federal budget, has been under regular peril since the 1970s from conservative lawmakers, who often decry what they view as the liberal bent of public media.

Jay H. Pearce, the chief executive of WVIK-FM in Rock Island, Ill., which receives about 15 percent of its budget from the federal government, said he was also concerned about problems with raising money. He pointed to broader cuts under consideration for federal arts and humanities financing, noting that many groups would have to compete against one another for private contributions to make up the difference.

“This year, everybody might rally, we might find the money,” Mr. Pearce said. “But what will happen next year, and the year after?”

Executives in public broadcasting were on alert since early this year, when rumors of major cuts began circulating, and on Thursday they did not hesitate to fire back. Their top talking point: “$1.35 per citizen,” an approximation of the annual cost to each American for providing a spectrum of public-interest shows.

“It’s not like cutting this would have any appreciable effect on any taxpayer across the country, but losing PBS would,” Neal Shapiro, president of WNET in New York, said in an interview. “In a lot of markets, the only place for real in-depth local coverage is the PBS station, the only place for arts and culture, the only place for safe harbor for kids.”

Ira Glass, host of “This American Life,” which does not receive any federal money, said, “Big stations in big cities will certainly be fine, especially in blue cities, where listeners will surely step up to replace any money that goes away.”

But the proposed cuts, Mr. Glass added in an email, could make it far more difficult for producers to begin ambitious new national programming. “If you’re starting a new news program, or anything with a public service mission,” he wrote, “C.P.B. is pretty much still the only game in town.”

Mr. Shapiro, of WNET, said city affiliates would eventually be hurt as much as rural stations. “If the beach washes out, the little houses go first,” he said, “but then the big houses go after that.”