In yet another testy Republican town hall on Wednesday, a 7-year-old ("almost eight") delivered a pointed warning to Sen. Tom Cotton (R) of Arkansas.

President Trump "is deleting all the parks and PBS Kids just to make a wall,” said Toby Smith inside the auditorium of Springfield High School in the Arkansas Ozarks. “Donald Trump thinks the wall is more important than kids' gains and stuff. But to kids, it’s more important.”

Toby, the last audience member to speak at the event, was apparently comparing the cost of a wall Mr. Trump has proposed building along the Mexican border, now estimated at $21.6 billion, to major cuts to the federal budget that his transition team proposed days ahead of his inauguration.

If the Trump administration and Republican-controlled Congress successfully privatize the Corporation for Public Broadcasting, the parent company of NPR and PBS, they will have achieved an end long sought by conservatives. Ever since its early days during the Nixon administration, the publicly funded television and radio stations have become a recurring subject of debate between Democrats and Republicans.

The argument is often framed around money: As more and more stations came on air and later online, why should Washington, with a budget in the trillions, fund a TV and radio station? Delve deeper, however, and the argument often boils down to ideology, as Gloria Goodale reported for The Christian Science Monitor in 2011.

That year, CPB’s public tab of $432 million was " 'nearly meaningless' in the face of America’s huge budget crisis,' Richard Levick of Levick Strategic Communications, a crisis and reputation management firm in Washington D.C., told Ms. Goodale. Efforts to end public funds for broadcasting are ideologically driven, he said.

In 2016, that tab increased to $445 million, or about 0.02 percent of the federal budget, as The Washington Post’s Ben Guarino calculated.

But the proposal from the Trump transition team to privatize the Public Broadcasting Service and National Public Radio are just two of the proposed massive cuts to the federal budget. A blueprint published in 2016 by the conservative Heritage Foundation, a think tank that helped staff the Trump transition team, sought to slash federal spending by $10.5 trillion over 10 years, according to The Hill. In addition to privatizing CPB, the proposed budget would eliminate the National Endowment for the Arts and the National Endowment for the Humanities, as well as shake up the funding of the Departments of Commerce and Energy.

When The Hill reported on the proposal in January, the document was expected to come out within 45 days of the inauguration. At this point, the administration’s full budget is expected in late April, after preliminary proposals are shared with federal departments and agencies.

PBS has weathered many threats to its federal funds from the right, starting with former President Richard Nixon. Public broadcasting began after the Kerner Commission, created by former President Lyndon Johnson to investigate the cause of the 1967 race riots, faulted broadcasters for failing to educate Americans about race, wrote Hugh Carter Donahue, then a researcher at MIT, in a 1995 column in the Monitor. From its inception, public broadcasting’s mission was to serve citizens through public education.

But PBS, as well as NPR, has been accused of leaning left. Only three years after PBS was created in 1970, Mr. Nixon vetoed CPB funding out of a conviction that programs such as PBS’s “Washington Week in Review” were biased against him, wrote Goodale.

That debate has regularly resurfaced.

After talk of defunding CPB came up in 1994 and 1995, a quiet, bipartisan effort tried to create a trust fund for public broadcasting, wrote Jerry Landay, a media observer and former ABC and CBS news correspondent.

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In 2011, the subject again came up, with both the House and Senate considering bills to eliminate funding to NPR and CPB. Driving much of that debate was a propaganda video from right-wing activists that purported to show NPR executives at a fundraiser calling tea party members “xenophobic” and saying NPR would be “better off in the long run without federal funding," Goodale reported.

Early justifications for public TV and radio no longer apply, they argue, because there are now so many more media options than back in the three-broadcast-network days. Supporters counter that public broadcasting still provides news coverage that is valuable and distinct in today’s media marketplace. Sure, the History Channel might nibble at a project from Ken Burns, the renowned documentary filmmaker who made his name with his 10-part Civil War series on PBS, but “when Ken says he wants 10 hours to do a series on Prohibition, they’d come back with ‘We’ll give you an hour,’ ” says Patrick Butler, president of the Public Media Association, a coalition of public radio and TV stations.

Similar arguments were repeated online on Thursday, in a comment thread on the Washington Post’s website. One commentator said PBS reporting reflects liberal ideologies, while some encouraged their fellow web surfers to rally behind the station.