While Republicans plot ways to slit its throat — hiding behind chants of fiscal responsibility — public broadcasting keeps shooting itself in the foot.

Clearly, if PBS and NPR are to be saved, it’s going to require a scheme sure to piss off everybody.

Here, then, is just such a plan: Transform “public broadcasting” into nonprofit broadcasting and supplant lost government funding — about $450 million a year to the Corp. for Public Broadcasting — by tapping into the commercial media.

Now, that sound you’re hearing is a piercing scream by the National Assn. of Broadcasters, along with the tinny sound of congressmen’s knees banging together, quaking at the thought of losing donations from that group and others. But hold on.

Money gleaned from the industry would not only be equitably apportioned, but these commercial interests would get something in exchange for their (coerced and reluctant) benevolence — namely, relaxation of public-interest and service rules, which most fulfill in pretty half-assed fashion anyway.

Unfortunately, PBS and NPR have been politicized. That those attacks currently come from elements like Fox News Channel — using an Orwellian tactic of trying to obscure its own partisan leanings by citing transgressions elsewhere — is, for this conversation, irrelevant. The bottom line is eliminating government funds would spare these stately institutions from being put on the chopping block every time a GOP senator objects to “Frontline,” or religious conservatives chafe (as they once did) at something like “Tales of the City.”

So where does public media come up with $450 million? Let’s start by asking “Viewers like you” to step up their commitment, even if that means more irritating pledge drives. Given the modest numbers who regularly patronize such fare, it seems reasonable to ask those who do to pick up a bit more of the tab.

The rest, though, would be siphoned from various TV interests as a tax (or “donation,” if you prefer). And the argument for that is simple: Commercial media often view community-service obligations — like offering educational programs for kids — as an onerous nuisance. So strip them of that requirement, let them run all the infomercials they want on Saturday mornings, and have them contribute to ensure “Sesame Street’s” availability on public TV.

Broadcasters hated the idea when I suggested it in the past, but it’s hard to understand why. Instead of airing 6 a.m. weekend talkshows that go unwatched, support nonprofit channels that will happily showcase the arts and public affairs and serve two groups the commercial marketplace neglects: the very young and the old.

Start by assessing an annual $2 fee per subscriber of cable systems and satellite operators — a drop in the bucket, given the $1,200 or so I paid DirecTV last year. At 100 million wired homes, that’s nearly half the necessary financing right there.

Next, consider the upfront marketplace, where the broadcast and cable networks sold more than $17 billion in combined commercial time last spring. Assess a small amount — say, half a percent — split among networks and media buyers for those transactions, and you’ll have another $90 million or more.

Finally, there are the U.S.’ commercial broadcasters — encompassing 1,750 TV stations and 13,000 radio outlets, according to the NAB. A donation from each of them to underwrite public TV and radio — in exchange for phasing out children’s and community requirements — would average about $7,500 each to make up the $110 million difference.

In the name of fairness, those fees would be weighted based on market size, so stations in New York and Los Angeles (which reach 7.5 million and 5.7 million homes, respectively) would foot more of the bill than the smallest markets in North Platte, Neb. (15,000), or Glendive, Mont. (4,000).

Broadcasters could plead their case for additional credit by demonstrating how inordinately civic-minded they are, but be warned: If your lineup includes “TMZ” and “Maury,” interviewing nuns the rest of the day won’t provide absolution.

And with that (and nonprofit tax breaks), PBS and NPR are paid for — saving Big Bird, “The Newshour” and “All Things Considered,” while eliminating whining about public money going to programs that don’t parrot Rush Limbaugh.

Could such a thing happen? Not likely — mostly because it makes too much sense.