A test of Trump's influence in a range of races and GOP hopes to flip a Senate seat: primary takeaways

Races stretching from Maine and South Carolina to Nevada and North Dakota on Tuesday tested former President Donald Trump's influence not just on the Republican Party but also on the way Americans regard voting and elections.

The Nevada Republican primary for U.S. Senate decided who will take on incumbent Democratic Sen. Catherine Cortez Masto in the general elections in November.

She is one of the most vulnerable Democrats this fall in a race that could determine who controls the upper legislative chamber and, with it, the fate of the remaining half of President Joe Biden's term.

A special election in South Texas could be a warning to Democrats and their thin congressional majority, and there were jousts between Trump-backed and Trump-opposed contenders, spotlighting how much of the primary season is about the GOP's future and the former president's role.

Here are some of the prominent outcomes.

GOP eyes Nevada to flip Senate

Former Nevada Attorney General Adam Laxalt won that state's Republican primary, setting up one of the most critical contests of 2022. Democrats, who can rely on Vice President Kamala Harris' tiebreaking vote in a Senate divided 50-50, cannot afford to lose a single seat this fall as it would cost them their slim majority.

Laxalt is an attractive contender across the GOP, supported by Trump and Senate Minority Leader Mitch McConnell, R-Ky. (who have been at odds since 2020).

The Silver State's Senate contest is one of four rated a toss-up by political forecasters this year, and three of those seats are held by Democrats.

Cortez Masto was going to face an uphill battle no matter who won the GOP nomination because of spiraling inflation and Biden's unpopularity.

A Suffolk University poll in April found 72% of Nevada voters said the state's economy was fair or poor.

Asked about the president's performance, 59% said they disapprove, and nearly half of voters – 47% – said their vote this fall will be about changing the direction Biden is leading the country.

Supreme Court: In Nevada, ruling on abortion rights could upend a Senate battle

False fraud accusations persist

Trump's false claims that the 2020 presidential election was stolen continue to haunt the country in down-ballot races.

In Nevada's Republican secretary of state race, Jim Marchant won the primary over six rivals, according to race calls by The New York Times and The Washington Post. 

Marchant is among a slate of candidates seeking the chief election officer spot in battleground states who say – wrongly – that fraud played a role in Biden's win.

Nevada Secretary of State Barbara Cegavske, a Republican, has repeatedly defended Biden's victory in the state, saying there was no evidence of widespread voter fraud in the 2020 election.

Marchant espoused conspiracy theories about the outcome, telling an audience during a forum in February that their vote "hasn’t counted for decades."

2022 midterms: A new 'Big Lie' battleground will be secretary of state elections

Trump 1-for-1 in South Carolina

South Carolina's GOP primary presented voters with another test of Trump's influence, this time against two House incumbents who defied the former president.

Republican Reps. Nancy Mace and Tom Rice faced primary challengers after criticizing Trump for his role in the insurrection Jan. 6, 2021, when a mob of Trump's supporters angry about his election loss invaded the Capitol.

Mace drew the former president's ire by voting to certify Biden's 2020 victory. She sought forgiveness by filming a campaign ad outside Trump Tower this year, saying she was one of his "earliest supporters" in 2016.

The early results showed Mace defeating former state Rep. Katie Arrington with more than the 50% needed to avoid a runoff.

Rice was among the 10 House Republicans who voted to impeach Trump after Jan. 6. Rice was unapologetic about his vote against Trump even though he knew it might cost him reelection.

That vote attracted a swarm of six GOP challengers who took on Rice in South Carolina's 7th Congressional District, which Trump won by roughly 18% in both of his presidential campaigns.

Rice was pummeled by state Rep. Russell Fry across the eastern South Carolina district. He received less than 25% compared with Fry, who won with a little more than 51% when the race was called Tuesday evening.

South Carolina primary: GOP Rep. Mace tries to woo Trump voters

Texas gives a warning to Democrats

When Rep. Filemon Vela, D-Texas, resigned in March to join a lobbying firm, it ignited a frenzy among political insiders over the special election to replace him.

National Republicans poured money into the heavily Hispanic district – which won't exist next year after redistricting – seeing a chance to increase their support in South Texas among minority voters and boost their chances in the midterms.

The bet paid off as results showed GOP contender Mayra Flores defeated Democrat Dan Sanchez.

Flores is already the Republican nominee in the newly drawn district, where she will face Democratic incumbent Vicente Gonzalez this fall.

This article originally appeared on USA TODAY: Primary takeaways: Nevada, South Carolina, and more