When Liz Cheney left the podium at a Wyoming ranch on Tuesday night, clapped and cheered by supporters, a Tom Petty song boomed out beneath the Teton mountains: “Well, I won’t back down / No, I won’t back down / You could stand me up at the gates of hell / But I won’t back down.”

The woman who has emerged as Donald Trump’s most implacable Republican adversary had suffered a landslide defeat in a primary election to decide Wyoming’s only seat in the US House of Representatives.

But unlike the former president, who loves to play victim, Cheney refused to dwell in political martyrdom after her act of self-sacrifice. In a 15-minute speech beside a dozen hay bales, a red vintage Chevrolet truck and four US national flags, she made clear that, while Trump had won the battle, the war for the soul of the party rages on.

“This primary election is over,” Cheney acknowledged to a crowd that, with aching symbolism, included her father, former vice-president Dick Cheney. “But now the real work begins.”

She invoked Abraham Lincoln, who lost congressional elections before ascending to the presidency and preserving the union. The vice-chair of the congressional January 6 committee warned that Trump and his enablers pose an existential threat to democracy and urged Americans of all stripes to unite.

To many in the crowd – who had wined and dined in a hospitality tent with a country and western band for entertainment – it sounded awfully like the launch of a presidential campaign.

Heath Mayo, 32, a lawyer, said: “On the question about the future of the party, there are few people making an argument counter to the prevailing Trumpism argument. She’s the only one that can make it. I hope she runs for president in 2024. She needs to be on that stage making that argument again, even if she loses. Keep making the argument.”

Carol Adelman, 76, who hired a 22-year-old Cheney for the US Agency for International Development, said that “of course” she would like see Cheney run for the White House in 2024. Alan Reid, 60, who works in finance, agreed: “Who else? Who’s better? I don’t see anybody from any party that shows the leadership that Liz shows.”

Cheney’s political future became a little clearer on Wednesday when she launched a leadership political action committee with the name “The Great Task”. Her spokesperson told the Politico website: “In coming weeks, Liz will be launching an organization to educate the American people about the ongoing threat to our Republic.”

In a TV interview, Cheney confirmed that she is “thinking about” a run for president in 2024 and will make decision “in the coming months”.

As the fall of the Cheney dynasty in Wyoming demonstrated, she would stand almost no chance of winning a Republican primary. But if the field is crowded and divided, for example between Trump, the Florida governor, Ron DeSantis, and former vice-president Mike Pence, she could make a symbolic impact in the “moderate” lane.

And as the January 6 hearings have shown, Cheney would relish nothing more than standing on a debate stage with Trump and prosecuting the case against him directly in prime time.

Alternatively, the three-time congresswoman could run as an independent candidate in the general election. This could peel crucial moderate votes away from Trump in battleground states, helping his Democratic opponent, presumably President Joe Biden.

But there might also be a danger that she would take votes from Biden, in particular those crossover Republicans who supported him in 2020 because of their hostility to Trump. Democrats would be anxious to avoid a repeat of 2000 when the third party “spoiler” Ralph Nader was blamed for costing Al Gore the election.

Cheney, who has vowed to do whatever it takes to keep Trump out of the Oval Office, would be equally wary of such a scenario unless, as some critics suspect, ambition and ego are competing with her nobler impulses.

Robert Talisse, an expert in contemporary political philosophy at Vanderbilt University in Nashville, Tennessee, wrote in an email: “If Cheney seeks the GOP nomination against Trump, she’ll be crushed. If Trump’s not seeking the nomination, he’ll still get to select the nominee.

“If she runs as an independent against Trump, she’ll probably siphon off a significant number of conservative voters who won’t be able to bring themselves to vote for a Democrat, but also can’t bring themselves to vote for Trump.”

The calculation would take place in the context that reports of Trump’s weakening grip on the Republican party have been greatly exaggerated. She is one of 10 House Republicans who voted to impeach him: eight have lost their primary or retired, while only two stand a chance of surviving to the next Congress.

Indeed, as Cheney exits the stage, at least for now, Sarah Palin, who paved the way for Trump, is making a comeback. On Tuesday, with his endorsement, she advanced to the November general election in the race for Alaska’s lone House seat. The journeys of these two fiftysomething women neatly sum up where the Republican party is at.

But as Cheney noted in her remarks, pro-Trump election deniers are rising all over the country. It has proved a winning formula in primaries that reward the loudest voices but could yet backfire on the party in the midterm elections, where centrist voters are put off by extremism. Republicans may blow their chances in the Senate with several radical candidates who are heavy on celebrity but light on gravitas.

For now, Trump will feel that Tuesday demonstrated that revenge is a dish best served Maga. But Adam Kinzinger, Cheney’s Republican colleague on the January 6 committee, is confident that she will not yield. Echoing Tom Petty, he told the MSNBC network: “She’s very determined, very dogged, and she will chase Donald Trump to the gates of hell.”