Rep. Paul Ryan (R-Wis.), the architect of his party’s radical plan to turn Medicare into a voucher program, gave a lesson Sunday in stating the obvious: “I don’t consult polls to tell me what my principles are or what our policies should be.” I’d suggest that Republicans with less disdain for public opinion might want to check out the height of the cliff from which Ryan would have them leap.

What concentrates the minds of GOP strategists and candidates — or ought to — is the spectacle unfolding in New York’s 26th Congressional District near Buffalo. It’s a solid Republican constituency, one that Chris Lee won last year with 74 percent of the vote. Alas, Lee resigned after a Web site published a bare-chested beefcake photo he had sent to a woman he met through Craigslist.

This meant there had to be a special election, scheduled for Tuesday. The Republican candidate, state Assemblywoman Jane Corwin, who has all the right credentials, had been expected to win easily. But she is in a tough battle with a strong Democratic challenger, Erie County Clerk Kathy Hochul — and last week, a stunning Siena College poll showed that Hochul had actually pulled ahead, 42 percent to 38 percent.

What should worry Republicans is that the biggest issue in the campaign — practically the only issue — is Ryan’s Medicare plan. Corwin supports it, Hochul opposes it, and the GOP may well lose a race that shouldn’t even be close.

Even if Corwin pulls out a victory — the national party has poured in buckets of money, allowing her to outspend Hochul by more than 2-to-1, and grandees such as House Speaker John Boehner have rushed in to campaign on her behalf — the fact that she is in such a tight battle is a dire omen for her party. Have I mentioned that all but four House Republicans have not just endorsed, but actually voted for, the Ryan plan?

Anyone who enjoys whistling past graveyards is free to note that the Corwin-Hochul contest is complicated by a third candidate, Jack Davis, running on the Tea Party line. The Pollyanna-ish view is that there are effectively two Republicans in the race, splitting the GOP vote. This is mitigated, however, by the fact that Davis has run for the seat twice before, in 2004 and 2006, and come pretty close to winning — both times as the nominee of the Democratic Party. The perhaps more realistic view is that there are effectively two Democrats in the race, and that if Davis were not running, Hochul might be doing even better.

Is the Medicare issue really that toxic? Newt Gingrich clearly thought it was, or else he’d never have called it “right-wing social engineering” and gotten himself in such trouble with his fellow Republicans. Even now, after a week of rhetorical beat-downs from GOP opinion-makers and busy signals from big-time donors, he’s still trying to find a way to support the Ryan plan while leaving some sure-to-be-needed wiggle room.

Leading Democrats, such as Senate Majority Leader Harry Reid, think the Ryan plan is toxic, too. Reid plans to hold a vote this week in which Republican senators will have to go on record as supporting, or opposing, the House-passed budget bill — which includes the Ryan plan to fundamentally transform Medicare as we know it. Minority Leader Mitch McConnell, seeing the trap that Reid has laid, says each GOP senator will be free to vote his or her conscience.

Many Republicans, sensibly, are eager to change the subject. This would be tough to do under any circumstances, given that the party has made the deficit its central issue. Moving along will be much harder with Democrats doing everything they can to keep the Ryan plan in the news — and with Ryan and other true believers still convinced that giving vouchers to senior citizens, putting them at the mercy of the private health insurance market, is a dandy idea that surely will catch on.

It won’t. Americans oppose Medicare cuts by overwhelming margins.

There are good reasons to believe the Ryan plan would have little, if any, real impact on the deficit. There are excellent reasons to believe it would do basically nothing to hold down soaring medical costs. And there is no reason to believe it is good politics — except for Democrats who explain to voters what Republicans prescribe for their golden years.

eugenerobinson@washpost.com