It's being billed as a "family feud," with ample quips about how Sunday's very public battle over gay marriage will make for an uncomfortable Christmas or Thanksgiving at the Dick Cheney household. But for those of us outside the Cheney family this is, first and foremost, a political issue. And the politics for Liz Cheney — who's trying to unseat Sen. Mike Enzi (R-Wyo.) in a Republican primary — are terrible.

Cheney is running as a more conservative opponent to Enzi, and a pro-Enzi super PAC released an ad in Wyoming last month questioning whether Cheney is opposed enough to same-sex marriage. The pretext of the ad is Cheney's opposition to a constitutional amendment banning gay marriage and support for same-sex couples getting benefits at the State Department. But the obvious subtext is that Cheney's 44-year-old sister, Mary Cheney, is married to a woman, Heather Poe.

A rift opened up between the once very close Cheney sisters in August, when Liz Cheney, 47, declared her candidacy — and opposition to same-sex marriage. The sisters haven't spoken since. On Fox News Sunday, Liz Cheney reiterated her belief in "the traditional definition of marriage," adding: "I love Mary very much. I love her family very much. This is just an issue on which we disagree."

Heather Poe expressed her annoyance on Facebook:

I was watching my sister-in-law on Fox News Sunday (yes Liz, in fifteen states and the District of Columbia you are my sister-in-law) and was very disappointed to hear her say "I do believe in the traditional definition of marriage."

Liz has been a guest in our home, has spent time, and shared holidays with our children, and when Mary and I got married in 2012 — she didn't hesitate to tell us how happy she was for us. To have her now say she doesn't support our right to marry is offensive to say the least.

I can't help but wonder how Liz would feel if as she moved from state to state, she discovered that her family was protected in one but not the other. I always thought freedom meant freedom for EVERYONE. [Facebook]

In case there were any question whether this was a unanimous opinion in the Cheney-Poe household, Mary Cheney "shared" Poe's post on her own Facebook feed with this personal note: "Couldn't have said it better myself. Liz — this isn't just an issue on which we disagree — you're just wrong — and on the wrong side of history."

There is a positive way to spin this public battle for Liz Cheney: Same-sex marriage isn't popular in Wyoming, especially among the Republican primary voters Cheney needs to come out for her at the polls. How better to prove her opposition to gay marriage than to publicly oppose her own sister's right to marry?

But among the people who don't believe that is Liz Cheney, says Jonathan Martin at The New York Times. She is reportedly "irritated that her sister is making their dispute public and believes it is hypocritical for Mary Cheney to take such a hard line now, given that she worked for the re-election of President Bush, an opponent of same-sex marriage."

The Wyoming primary race is already unusually personal, replete with charges of Cheney being a carpetbagger and a dinner-party spat between Liz's mom, Lynne Cheney, and former Sen. Alan Simpson (R-Wyo.), who thinks Cheney's run is disastrous for the party.

This new "ugly family drama and questions about what Liz Cheney truly believes could reinforce questions about her authenticity in a place where many voters have met their politicians in person and are already skeptical of an outsider like Ms. Cheney," says Martin at The New York Times. Mary Cheney knows this, too, but says she will continue making an issue of her sister's stance on gay marriage.

"What amazes me is that she says she's running to be a new generation of leader," Mary Cheney tells the Times. "I'm not sure how sticking to the positions of the last 20 or 30 years is the best way to do that." And when Martin pointed out that "such criticism could complicate her sister's Senate campaign, Mary Cheney offered a clipped answer reminiscent of her father's terse style. 'OK,' she said, before letting silence fill the air."

No matter who wins, Enzi or Cheney, Wyoming will be represented by an opponent of same-sex marriage. Judging by early polls, the voters are sticking with Enzi. Policywise, this public dispute could show us how much potency gay marriage still holds on the right. If Enzi and his backers continue to poke Cheney on the issue, presumably that means their polling tells them it's working. If they drop it, it could be seen as another sign that even in dark-red Wyoming, gay marriage is losing its power as an electoral cudgel.

That said, it really should be an awkward Christmas at the Cheney family get-together in Jackson Hole. According to The New York Times, Dick and Lynne Cheney will spend Thanksgiving at Mary Cheney and Heather Poe's home in Northern Virginia, but the whole Cheney clan will spend Christmas in the Wyoming town where Liz Cheney now calls home. "I will not be seeing her," Mary Cheney says of her sister.

Dick Cheney, who more or less supports the right to gay marriage, has (probably wisely) decided to stay out of the fight as much as possible. The relevant portion of his conversation with CNN's Jake Tapper starts at the 4:54 mark: