The invitation looked like something drawn up by John Hodgman’s ascot-wearing fat cat on “The Daily Show.”

Except that this was no fictional Republican stereotype created for comic relief. This was the real thing – Erie County-style.

The flier for the “Cigar Smoker” fundraiser for the Erie County Republican Committee featured a smoldering fat cigar complete with a wisp of smoke billowing upward and, of course, a glass of cognac. What would a plutocrat be without his cognac?

Democrats couldn’t have designed a better promo – if the idea was to paint the GOP as hopelessly out of touch with working-class Western New Yorkers.

Even as they are gifted the keys to the political kingdom – from a trifecta of Obama administration controversies to the Assembly’s sexual-harassment cover-up to the mishandling of sensitive Erie County social services records – Republicans don’t know how to get out of their own way. Puffing cigars and sipping cognac in a swanky restaurant is hardly the way to tell the little people you’re looking out for them.

After the embarrassment of Mitt Romney’s “47 percent” candor, any reasonably in-touch GOP operative should be sensitive to the image created by such a pitch. So it’s hard to say which is worse: being that out of touch, or seeming not to realize you’re that out of touch. County GOP Chairman Nicholas Langworthy seems guilty of both.

“They sell cigars in all different prices. … People in all walks of life a enjoy a good drink and a cigar once in a while,” he said. Langworthy dismissed any image concerns, as if Tuesday night’s event was nothing more than Joe the Plumber having a smoke.

“We have all sorts of different events,” Langworthy added, mentioning barbecue fundraisers as another – presumably less highbrow – example.

Sharing “premium cigars & spirits” in the Black Rock waterfront restaurant cost $150 per person, $500 for sponsors or $1,500 if you wanted to join the Chairman’s Club. A mere $5,000 would buy you a seat on the Republican Leadership Council.

Of course, Democrats also raise obscene amounts of money through ritzy fundraisers in a political system open to the highest bidders. But they aren’t the ones fighting the patrician image. Optics matter, especially when you’re the party typecast as looking out for the 1 percent.

And the stereotype isn’t far off as long as the GOP writes off a poor city such as Buffalo in order to suppress turnout rather than actively competing for those votes by projecting an “everyman” image and policies to match.

Instead of the puff fest, imagine a GOP fundraiser at Johnnie B. Wiley Stadium with part of the proceeds going to the facility the city schools are struggling to maintain. Imagine the message that would send to city voters tired of being held hostage by Democrats.

One organizer described the cigar get-together as “just a fun event.” But the symbolism of it makes clear that the GOP needs to pick its fun a little more strategically.

Unless, of course, Langworthy is right. Unless there is no image problem. Unless this is what the party really is.