On one of the most consequential nights of the US primary season, amplifiers of Donald Trump’s stolen-election myth won in Arizona and Michigan – in the latter state defeating a Republican who voted for Trump’s impeachment – while voters in Kansas decisively rejected an attempt to remove abortion protections from the state constitution.

With fewer than 100 days left before the November midterm elections, the results confirmed Trump’s grip on Republican voters and advanced his efforts to purge critics and elevate loyalist standard-bearers.

The verdicts rendered on Tuesday night are likely to have major implications for both parties.

Democrats face a difficult election cycle, hampered by Joe Biden’s low approval ratings and widespread dissatisfaction with leadership in Washington in the face of economic problems. Historically, the opposition party makes gains in the first midterms of any presidency, often by framing the election as a referendum on the president.

With narrow majorities in Congress, Democrats cannot afford to lose any seats in the Senate and only a handful in the House. But party leaders were hopeful on Tuesday that the abortion rights verdict in Kansas might energize voters and boost Democrats in close contests to come.

Another midterm strategy employed by Democrats – boosting far-right candidates in Republican primaries in the hope of facing weaker opponents in November – met with success, despite bipartisan warnings that the approach could backfire, with dangerous consequences for US democracy.

In a congressional primary in Michigan, John Gibbs defeated Peter Meijer, the Republican incumbent who was one of 10 House Republicans to vote to impeach Trump over the Capitol attack, after Democrats ran ads highlighting Gibbs’s pro-Trump credentials.

In a statement, Meijer said: “I’m proud to have remained true to my principles, even when doing so came at a significant political cost.”

But he published angrier words on Monday, assailing Democrats who spent heavily in support of Gibbs.

In an online essay, Meijer wrote: “The Democrats are justifying this political jiu-jitsu by making the argument that politics is a tough business. I don’t disagree.

“But that toughness is bound by certain moral limits: those who participated in the attack on the Capitol, for example, clearly fall outside those limits. But over the course of the midterms, Democrats seem to have forgotten just where those limits lie.”

Meijer was the second Republican who voted to impeach to lose a primary contest. Four have opted to retire rather than to seek re-election. Two others were on the ballot on Tuesday in Washington state. Jaime Herrera Beutler and Dan Newhouse were in close races against Trump-backed challengers which had yet to be called.

So far, only one Republican who voted to impeach Trump, David Valadao of California, has survived, with a narrow victory in California.

Michigan also saw a Trump-backed candidate win the Republican nomination for governor. Tudor Dixon, a conservative media personality, will face the Democratic governor, Gretchen Whitmer, in November.

In an incumbent-on-incumbent Democratic primary for a newly redrawn Michigan House district, Haley Stevens, a moderate backed by the political arm of the American Israel Public Affairs Committee, defeated Andy Levin, a progressive from a prominent political family. Elsewhere, progressive members of “the Squad”, Rashida Tlaib in Michigan and Cori Bush in Missouri, beat back moderate challengers.

In Arizona, a battleground state that became the epicenter of election denialism in the wake of Biden’s 2020 victory, the Trump-endorsed Blake Masters won a crowded Republican primary to face Mark Kelly, the Democratic incumbent, in a contest that could determine control of the US Senate.

In the race for Arizona secretary of state, a post that oversees elections, Republicans nominated Mark Finchem, a self-identified member of the far-right Oath Keepers militia who has amplified false claims about the 2020 election and was backed by Trump.

The Republican primary for governor was too close to call but by Wednesday Kari Lake, a former TV anchor backed by Trump, was narrowly leading Karrin Taylor Robson, backed by the former vice-president Mike Pence.

Trump’s quest for retribution against Republicans who crossed him gained a win when Rusty Bowers, Arizona’s Republican House speaker, who rose to prominence when he testified to the House committee investigating the January 6 insurrection, lost his bid for a state Senate seat to David Farnsworth, who had Trump’s support.

In Missouri, where Trump urged voters to choose “Eric” without specifying which in a Senate primary contest with three Erics, Republican leaders were relieved it was Eric Schmitt, the attorney general, who emerged victorious.

Eric Greitens, the scandal-plagued former governor who resigned in 2018 and was attempting a political comeback, finished third. Schmitt will now face Trudy Busch Valentine, a deep-pocketed beer heiress who Democrats nominated over the more populist Lucas Kunce.

Though Trump’s endorsement record is mixed, his string of victories on Tuesday night underscored conservatives’ enduring allegiance to the former president despite a stream of damaging revelations about his efforts to overturn the election and his conduct during the deadly assault on the Capitol.

Perhaps the most closely watched vote on Tuesday wasn’t an election, but a referendum. In the first test of the potency of abortion as electoral issue in the post-Roe era, voters in Kansas resoundingly rejected an amendment that would have erased the right to abortion from the state constitution.

The decisive vote in a state that voted overwhelmingly for Trump in 2020 is the first major electoral victory for supporters of reproductive rights since the the supreme court invalidated the constitutional right to an abortion in June.

It also serves as a warning to Republicans who have sought to downplay the significance of the issue in an election year otherwise dominated by inflation and economic woes.