Kristi Noem, the South Dakota governor and Republican vice-presidential hopeful, saw polling numbers plummet after the Guardian revealed that she writes in a new book about the day she shot dead a hunting dog and an un-castrated goat, a revelation that ignited a political storm.

Announcing what it called its “Noem Puppy Murder Poll Findings”, New River Strategies, a Democratic firm, said 81% of Americans disapproved of Noem’s decision to shoot Cricket, a 14-month-old wire-haired pointer who Noem says ruined a pheasant hunt and killed a neighbour’s chickens, thereby earning a trip to a gravel pit to die.

According to Noem’s account, the goat, which Noem did not name, followed Cricket to the pit because Noem deemed his odour and behaviour unacceptable on her farm. By Noem’s own detailed admission, it took two blasts from a shotgun, separated by a walk back to her truck for more shells, to finish the goat off.

Noem’s book – No Going Back: The Truth on What’s Wrong with Politics and How We Move America Forward – will be published in May. The Guardian obtained a copy.

The governor’s extraordinary admission made news because she has long been seen to be auditioning to be picked for vice-president by Donald Trump, the presumptive Republican presidential nominee.

On Friday, amid widespread disbelief that Noem chose to tell such a horrific story in such detail in a campaign book, most observers thought her chances of winning the Trump veepstakes were over.

Wrote Meghan McCain, a conservative pundit whose father, John McCain, in 2008 made one of the most disastrous vice-presidential picks of all time, in the form of extremist Sarah Palin: “You can recover from a lot of things in politics, change the narrative etc – but not from killing a dog.

“All I will distinctly think about Kristi Noem now is that she murdered a puppy who was ‘acting up’ – which is obviously cruel and insane. Good luck with that VP pick[,] lady.”

According to New River Strategies: “While 37% of Republicans are still not sure if [Noem] would be a good choice, 84% of them report liking or loving dogs – not a promising sign.”

Fourteen percent of respondents to the poll still thought Noem would be a good choice for vice-president to Trump. Among Republicans, 21% thought Noem would be a good pick, to 42% who did not.

Among self-identified “very conservative voters”, 28% said Noem would be a good choice, against 32% who said she would not.

New River noted: “A plurality of Americans who do not like dogs still disapprove of the governor’s action. While 87% of Americans who love dogs disapprove of what the governor did, so too do 48% of Americans who do not care for the animals.”

Politico, which reported the New River poll, also noted Noem had fallen in a ranking of potential Trump running mates offered by PredictIt, an online betting firm.

By Saturday, Noem had fallen from second, behind Tim Scott, the South Carolina senator, to fourth, also behind Elise Stefanik, the New York representative, and Tulsi Gabbard, a former representative and Democratic presidential hopeful whose own campaign book, out on Tuesday, does not contain any scenes of shooting puppies.

Noem responded to reports about her book by saying: “We love animals, but tough decisions like this happen all the time on a farm.” She added that her family recently put down three horses.

Her communications director, Ian Fury, cited polling showing Noem as the only potential Trump vice-presidential pick with a positive favourability rating in four battleground states: Arizona, Michigan, Pennsylvania and Wisconsin.

“This is why the liberal media is so eager to attack Kristi Noem,” Fury said. “She’s the potential running mate they fear most.”

The poll from Kaplan Strategies, which describes itself as bipartisan, was conducted the previous weekend but released on Friday, the day the Guardian broke the story of Noem, Cricket the dog and the unnamed goat.

On Saturday, the Guardian attempted to contact public figures whose glowing recommendations of Noem’s book are printed on its jacket and introductory pages.

In his blurb, Trump calls Noem “a tremendous leader, one of the best”, adding: “This book, it’s a winner … you’ve got to read it!”

Asked whether Trump had read the whole book before recommending it, and whether he had comment about the controversy over Noem’s tale of killing domestic animals, the former president’s spokesperson, Steven Cheung, did not immediately respond.

Fox News spokespeople did not immediately respond to a request for comment from Rachel Campos-Duffy, a host whose quote on Noem’s book salutes her “common sense and fearless fight for freedom”, adding: “Get ready to be inspired!”

No Going Back is also blurbed by Chaya Raichik, creator of the trolling Libs of TikTok social media account; James Golden, also known as Bo Snerdley, formerly sidekick to the late rightwing shock jock Rush Limbaugh; and Riley Gaines, a former college swimmer who campaigns against transgender participation in women’s sports.

By Saturday, Raichik had not commented about Noem’s dog-killing confession. Snerdley had reposted a Daily Mail version of the Guardian report.

Gaines, who calls Noem’s book “the perfect blueprint for young Americans on how to move our nation forward”, did not comment on the controversy over Noem’s decision to kill a 14-month-old dog. She did, however, post a video of eight puppies sleeping in a pile on a pink rug.

“The pups have arrived!” she wrote. “Be still my heart.”

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