"Since it has, one thing should be clear," the statement continued. "Liz has always believed in the traditional definition of marriage. She has also always treated her sister and her sister's family with love and respect, exactly as she should have done."
In Wyoming, scene of the murder of gay university student Matthew Shepard 15 years ago that remains a watershed moment for gay rights, Liz Cheney's stance mirrors the Equality State's own soul-searching on gay marriage.
The heavily Republican state Legislature has swung from close votes just a few years ago on proposals to ban recognition of gay marriages performed in other states to, this year, giving serious consideration to permitting same-sex civil unions and a ban on discrimination against gay people.
Liz Cheney's opponent Sen. Mike Enzi says he supports a constitutional amendment to define marriage as between one man and one woman, only.
For her part, Liz Cheney says gay marriage should be a matter for states to decide and supports the "traditional definition" of marriage. But she says she doesn't think states should discriminate against same-sex couples.
She has opposed a federal constitutional amendment to ban gay marriage and supported equal spousal benefits for same-sex couples employed by the State Department, where she used to work.
"I stand by both of those positions," she said on Fox News Sunday. "I don't believe we ought to discriminate against people because of their sexual orientation. If people are in a same-sex relationship, and they want their partner to be able to have health benefits or be designated as a beneficiary under life insurance, there's no reason we shouldn't do that."
But what if a state were allowed to ban gay marriage and, as a consequence, prohibit all the advantages, such as health insurance and death benefits, which marriage confers to heterosexual couples?
"The issue of sanctioning marriage has always been up to the states and to the people in the states and that is where it belongs. My own personal view is that marriage is between a man and a woman," she responded to The Associated Press by email.
How much attention the matter gets before Wyomingites cast their votes in their state's Republican primary nine months from now remains to be seen.
Mary Cheney and her wife, Heather Poe, didn't waste any time challenging Liz Cheney's television comments as insufficiently pro-gay 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," Poe posted on Facebook. "To have her now say she doesn't support our right to marry is offensive to say the least."
Chimed in Mary Cheney: "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," she posted.
Enzi was first elected to the US Senate in 1996 and is seeking a fourth term. He will continue to support legislation that "protects the institution of marriage," campaign spokeswoman Kristen Walker said by email Monday.
Many people informally call Wyoming the Cowboy State. Officially, it's the Equality State, so-named because it was first to allow women to vote, serve on juries and hold public office.
- AP