Originally Published: 14 JUN 22 18:33 ET

Updated: 15 JUN 22 14:10 ET

By Gregory Krieg, CNN

(CNN) -- South Carolina Republican voters on Tuesday split on two US House incumbents who defied former President Donald Trump, renominating Rep. Nancy Mace but souring on Rep. Tom Rice, the first of the 10 House Republicans who voted for Trump's impeachment last year to fall in a primary.

State Rep. Russell Fry, who was endorsed by Trump, will defeat Rice in the 7th District, CNN projects.

Despite facing a severe backlash over his impeachment vote, including death threats in its aftermath, Rice did not back off his criticism of Trump or decide, like some of his impeachment-backing GOP colleagues, to leave office at the end of his term rather than face voters again. A staunch conservative and Trump supporter before the insurrection, the five-term congressman instead took his case out on the campaign trail. Republicans in his 7th District rejected it -- and delivered the nomination to Fry, who will clear the 50% mark to avoid a runoff.

Rice's ouster underscores Trump's enduring popularity with most Republicans, especially in conservative districts like the one Rice has represented since 2013. But results in the 1st District demonstrated that the former President's hold is not entirely firm.

Mace did not vote to impeach Trump, but she refused to join congressional objectors to President Joe Biden's victory, earning the former President's wrath. Faced with charges of insufficient loyalty to Trump, she drew a challenge from Katie Arrington, who defeated then-Rep. Mark Sanford, another Trump critic, in the 2018 primary but went on to lose the general election.

Arrington, like Fry, had Trump's endorsement. But it wasn't enough. Mace will defeat Arrington in their three-candidate race, CNN projects. Mace had the backing of former South Carolina Gov. Nikki Haley, who served as UN ambassador in the Trump administration.

In a rare conciliatory move, Trump congratulated Mace but declared Rice's loss "the biggest News of the evening" in posts on his new social media platform.

Nevada, Maine, North Dakota and a special election in Texas' 34th Congressional District were also on the menu Tuesday, with the most fierce contests featuring Republicans vying for nominations ahead of a midterm general election that looks increasingly dire for Democrats trying to hold on to their narrow majorities in the US House and Senate.

Recent Democratic dominance in Nevada is in for a stress test in the fall from Silver State Republicans who are poised, after Tuesday night, to field a collection of general election candidates up and down the ballot who have embraced Trump's lies about the 2020 election to varying degrees.

Former state Attorney General Adam Laxalt will win the Republican nomination, CNN projects, to take on Democratic Sen. Catherine Cortez Masto, one of the most vulnerable Democratic incumbents.

Endorsed by Trump, he fended off a late push from political newcomer Sam Brown, a retired Army captain who received a Purple Heart after suffering severe burn injuries in Afghanistan.

Laxalt, whose late grandfather Paul Laxalt served as Nevada's governor and then as one of its US senators for two terms, had served as the former President's 2020 campaign co-chair in the state and peddled unsubstantiated allegations of voter fraud after Trump's loss there became apparent.

He lost his last bid for statewide office, the 2018 gubernatorial race. This year, he has the backing of Florida Gov. Ron DeSantis, former Secretary of State Mike Pompeo and other leading conservatives with eyes on the 2024 presidential race.

The contest for the GOP gubernatorial nomination, and a November date with Democratic Gov. Steve Sisolak, was particularly emblematic of the modern-day Republican Party -- all three candidates aligned themselves with Trump, a symbol of his movement's growing power. But it's Clark County Sheriff Joe Lombardo, the candidate with the former President's endorsement, who will win the GOP nomination, CNN projects, defeating former Sen. Dean Heller and Joey Gilbert, a lawyer and retired boxer.

In years past, the race to fill the seat of term-limited Republican Nevada Secretary of State Barbara Cegavske might have flown under the national political radar. But in the wake of Trump's bid to overturn the 2020 results -- efforts Cegavske dismissed -- and with more recent, successful Republican attempts to restrict ballot access in mind, Democrats are renewing their focus on offices that oversee elections.

Cisco Aguilar, an attorney and former staffer for the late Sen. Harry Reid, ran unopposed for the post in the Democratic primary. Former state Assemblyman Jim Marchant, who CNN projects will win the Republican nomination, filed an unsuccessful lawsuit after losing his 2020 House race and has said he would not have certified Biden's victory in Nevada if he'd been in Cegavske's seat after the election.

Down the ballot, a handful of the state's Democratic House members were facing primary challenges. Rep. Dina Titus will win renomination, CNN projects, defeating progressive challenger Amy Vilela, who was endorsed by Sen. Bernie Sanders last week. The Vermont independent won the Nevada caucuses during the 2020 Democratic presidential primary.

Down in Texas, the Tuesday night lights were on again, this time for a special election to finish out former Democratic Rep. Filemon Vela's term in the soon-to-be-former 34th Congressional District. Vela's resignation in late March to work for a law and lobbying firm opened the seat in a district Biden narrowly won in 2020 but that is poised to become more comfortably blue-leaning after redistricting comes into effect in the November election. The special election took place under the existing district boundaries.

Former Cameron County Commissioner Dan Sanchez, a Democrat, conceded to Republican Mayra Flores Tuesday night. CNN projected the race for Flores on Wednesday. Flores' win gives Republicans an additional seat in the House -- but only until January.

Republicans were heavily invested in the special election, hoping to give Flores -- already their general election nominee for the new district -- a head start in her coming race against Democratic Rep. Vicente Gonzalez, currently of the 15th Congressional District.

"Based on the results, we came up short tonight despite being outspent by millions of dollars from out of state interests and the entire Republican machine," Sanchez said in a statement. "Too many factors were against us, including too little to no support from the National Democratic Party and the Democratic Congressional Campaign Committee."

Flores will become the country's first Mexican-born member of Congress -- a piece of history Republicans are hoping to wield as a signal of the party's growing foothold with Hispanic voters in South Texas ahead of her clash with Gonzalez.

In Maine, more familiar faces dominated the primary night landscape.

Former Republican Gov. Paul LePage -- the man who once declared himself "Donald Trump before Donald Trump became popular" -- is on the general election ballot again as he seeks to win back his old job from Democratic Gov. Janet Mills, a longtime political foe. Both were running unopposed in their primaries ahead of another November showdown.

The Republican field was more competitive in the state's 2nd Congressional District, where the nominee will take on one of the Democratic Party's most endangered incumbents, Rep. Jared Golden. Former Rep. Bruce Poliquin, who lost his seat to Golden in 2018 after neither managed to secure a majority and the race was decided by Maine's ranked-choice system, will defeat Caratunk Selectwoman Liz Caruso in the primary, CNN projects.

There was less drama in North Dakota, where CNN projects Republican Sen. John Hoeven will win the nomination over conservative activist Riley Kuntz. Hoeven is expected to comfortably win reelection in November in the deep red state over Katrina Christiansen, who CNN projects will be the Democratic nominee.

This story has been updated with additional developments.