South Dakota GOP Gov. Kristi Noem has long been a potential running mate for former President Donald Trump, largely on the strength of her conservative credentials and the Republican Party's push to appeal to more female voters.

But Noem's admission that she killed her family's 14-month-old dog, Cricket, has elicited bipartisan outrage in recent days — and it could prompt Trump to look elsewhere should he be seriously considering Noem for the No. 2 slot.

In her forthcoming memoir, "No Going Back: The Truth on What's Wrong with Politics and How We Move America Forward," Noem wrote that she killed her dog because the dog was "untrainable" and "dangerous to anyone she came in contact with," according to an excerpt obtained by The Guardian.

Noem has continued to defend the act, stating last week on the Fox News program "Hannity" that the dog posed a threat to her children.

"She attacked me. And it was a hard decision," Noem said.

But according to a GOP senator who spoke to The Hill, Noem has sunk her chances with Trump.

"She's just done, too much drama," the unnamed lawmaker, who remains in contact with the former president, told the outlet.

Mike Rounds, one of Noem's Republican home-state senators, said the governor's actions could damage her in the eyes of voters should Trump select her to be his running mate.

"I don't see how it helps," the senator told CNN last week. "I've had dogs. I just think that when a family decides to put down dogs, it's a very personal and private decision to be made."

"These dogs become a member of a family, you know?" he continued. "People identify with that."

However, Dusty Johnson, the state's at-large GOP congressman, came to Noem's defense.

"I will tell you, there are lots of people in rural America, who if an animal's got to be put down, they would do that themselves," he told CNN. "I know most people would go to the vet, but I would tell you that Kristi Noem was not the first or the one thousandth, you know, farmer or rancher that's put down an animal themselves."

Noem, in late April, took to X to remark on the circumstances of such situations.

"We love animals, but tough decisions like this happen all the time on a farm," she wrote. "Sadly, we just had to put down three horses a few weeks ago that had been in our family for 25 years."

Business Insider reached out to a representative of Noem for comment.