The South Carolina congresswoman Nancy Mace easily survived a primary challenge on Tuesday, against Kevin McCarthy-backed Catherine Templeton, while a much closer than expected special election in Ohio offered warning signs for Republicans ahead of November.

In Ohio’s sixth district, candidate Michael Rulli prevailed in the special election to replace fellow Republican Bill Johnson, who resigned from Congress in January. Rulli’s victory will help expand his party’s razor-thin majority in the House, but his nine-point win over Democratic contender Michael Kripchak may unnerve Republicans, given that Donald Trump carried the district by 29 points in 2020.

In South Carolina, McCarthy, the former House speaker, attempted to oust Mace by backing her rival, but the the two-term incumbent received a crucial endorsement from Trump. The grudge match was personal for McCarthy, as Mace was one of the eight Republicans who voted to oust the then speaker last year.

The high stakes made the race a costly one, with outside groups dumping millions of dollars into the district. The South Carolina Patriots Pac spent nearly $4m backing Templeton’s primary bid, while the Win It Back Pac and Club for Growth Action collectively invested roughly $2.5m supporting Mace. Despite Templeton’s external support, Mace led by 29 points when the Associated Press called the first congressional district race about an hour and a half after polls closed in South Carolina.

Mace was not the only South Carolina Republican facing a primary threat on Tuesday. Over in the fourth district, the Republican congressman William Timmons was running neck and neck with state representative Adam Morgan, who leads the South Carolina legislature’s freedom caucus. Like Mace, Timmons had the benefit of Trump’s endorsement, but the race was still too close to call three hours after polls closed.

And at least one of South Carolina’s House Republican primaries will advance to a runoff later this month. In the reliably Republican third district, Trump-backed pastor Mark Burns and Air National Guard Lt Col Sheri Biggs will compete again on 25 June to determine who will have the opportunity to succeed Jeff Duncan, the retiring representative.

Meanwhile, the fate of South Carolina’s abortion laws rests in part on the results of three Republican primaries in state senate races. State senators Katrina Shealy, Margie Bright Matthews, Mia McLeod, Sandy Senn and Penry Gustafson collectively blocked a near-total abortion ban in South Carolina earlier this year. The “Sister Senators” were feted as a profile in courage by the Kennedy Center, but the three Republicans among them – Shealy, Senn and Gustafson – face primary challengers from their right on abortion. If two of the three lose to challengers, abortion foes will have the votes to restrict abortion beyond the current six-week ban.

In addition to South Carolina, three other states held primaries on Tuesday. In Maine’s second congressional district, the former Nascar driver turned state representative Austin Theriault resoundingly defeated fellow state representative Michael Soboleski in the Republican primary. Theriault will advance to the general election against Democratic congressman Jared Golden, who faces yet another difficult re-election campaign.

Republicans are hopeful that Theriault has the résumé to defeat Golden, but the Democrat has proven politically resilient since he was first elected to Congress in 2018, when he narrowly defeated the Republican incumbent, Bruce Poliquin, thanks to Maine’s ranked-choice voting system. In 2022, Golden again defeated Poliquin by six points in the second round of voting, even though Trump had carried the second district by seven points two years earlier.

The Cook Political Report rates Golden’s seat as a toss-up, so Theriault’s victory will kick off what is expected to be a heated and closely contested race in the general election. Just minutes after the AP made Theriault’s primary win official, the left-leaning Pac American Bridge 21st Century began attacking him over his views on abortion access.

In Nevada, a dozen Republicans are vying for their party’s Senate nomination, but the primary appears to have become a two-person race between the retired army captain Sam Brown and former US ambassador to Iceland Jeff Gunter. Polling indicates Brown has a significant lead over Gunter, and Brown has received a last-minute boost from Trump, who made a much-awaited endorsement in the race on Sunday.

The winner of the Republican primary will go on to face the Democratic incumbent, Jackie Rosen, in one of the most closely watched Senate races this year, as the Cook Political Report rates the seat as a toss-up.

Further down the ballot, the Democratic congresswoman Susie Lee faces a tough re-election campaign in Nevada’s third congressional district. Seven Republicans – including video game music composer Marty O’Donnell and former state treasurer Dan Schwartz – are running for the chance to face off against Lee, but Trump has stayed out of the primary so far. The former president’s only House primary endorsement in Nevada went to the former North Las Vegas mayor John Lee in the fourth district, but the winner of that race will face a much steeper climb to defeat the Democratic incumbent, Steven Horsford, in the general election.

Over in North Dakota, five Republicans and two Democrats are running to replace the Republican congressman Kelly Armstrong representing the state’s at-large congressional district, but no Democrat has won the seat since 2008. Rather than seeking re-election, Armstrong has launched a gubernatorial bid, and he won his primary on Tuesday. Armstrong is widely favored to replace the outgoing governor, Doug Burgum, who has been named as a potential running mate for Trump.

North Dakota voters also weighed in on a ballot measure regarding age limits for congressional candidates. If approved by a majority of North Dakota voters, the measure would prevent candidates from running for Congress if they would turn 81 during their term. Although the policy would only apply to congressional candidates, the age cutoff is noteworthy considering Joe Biden, who is four years older than Trump, turned 81 in November.