Attention, people, this is important: The battle over whether it’s true that the Republican plan would “end Medicare” is about to play out in a critical way in New Hampshire.

The National Republican Congressional Committee, which oversees House races for the GOP, has written a sharply-worded letter demanding that a New Hampshire TV station yank an ad making that claim. Whether the ad gets taken down could help set a precedent for whether other stations will air Dem TV ads making this argument, which is expected to be a central message for Dems in the 2012 elections.

The NRCC letter was provided to me by the Progressive Change Campaign Committee, which is airing the ad on WMUR against GOP Rep. Charlie Bass. The letter — which calls on Comcast Boston to take down the ad and is unusually detailed and emphatic — reflects how badly Republicans want a halt to these Dem attacks. Here’s the letter’s core argument:

The Budget Resolution as approved by the U.S. House of Representatives does NOT end Medicare. In fact, the Budget Resolution makes no changes at all to Medicare for current or near retirees, as none of the Medicare-related provisions in the Budget Resolution would even take effect until 2022. This fact makes the Advertisement especially misleading, as the woman featured in the Advertisement is a current Medicare beneficiary, and would not have her Medicare benefits ended, or even changed in any way, under the Budget Resolution... Additionally, the Budget Resolution ensures that Americans aged 54 and younger will still have Medicare when they retire by implementing a new, sustainable model of Medicare. This new version of Medicare would actually REQUIRE insurance companies to GUARANTEE coverage for seniors.

The letter argues that the claim that Republicans would “end Medicare” is “blatantly and wholly false, and has been deliberately crafted to mislead and frighten voters.” It also cites a recent Politifact analysis that pronounced the assertion “highly misleading.”

But there are plenty of people making the opposite case: That the GOP plan does, in fact, end Medicare. The argument is that the GOP plan would do away with the current, single payer, government-run system that guarantees payment for your major health care costs as you move into retirement. The GOP proposal would replace this with a system in which government gives premium support — that could over time fall short of health care costs — to seniors to purchase their own private plans. In other words, the new plan does away with the program we now call “Medicare” and replaces it with a different program — and hence “ends” it.

“The plan would replace our current system, in which the government pays major health costs, with a voucher system, in which seniors would, in effect, be handed a coupon and told to go find private coverage,” Paul Krugman wrote recently. Similar cases have been made by Steve Benen , Josh Marshall, and Atrios, among others.

“There’s nothing even slightly misleading about calling this an effort to end Medicare,” Matthew Yglesias wrote recently, adding that it’s “important for all progressives on the Internet to draw a line in the sand under this one.”

The GOP demand that Comcast Boston yank may give progressives a chance to draw that line — but if the ad does get pulled it could become tougher for Dems to amplify the claim going forward. This is an important test case, and it’ll be interesting to see how this plays out.

UPDATE: Here’s video of the PCCC/ Democracy for America ad:

UPDATE II: Post edited slightly from original.

UPDATE III: Comcast has rebuffed the GOP demand and will continue running the ad. Still waiting on WMUR.