The 'big lie' loomed over Tuesday's primaries in Nevada, South Carolina

As the House Jan. 6 committee's latest hearings ramp up, a set of primary races on Tuesday featured a slate of Donald Trump-endorsed candidates who support the same "big lie" about the 2020 election that investigators say fueled last year's insurrection at the Capitol and an "attempted coup."

The primary featured races for Senate, House and gubernatorial seats in Nevada, South Carolina, North Dakota and Maine. Texas held a special election for its 34th Congressional District seat.

Many of the races in Nevada included candidates who support the former president's evidence-free claims that the 2020 election was stolen, while two House candidates in South Carolina who were critical of Trump's role in Jan. 6 or supportive of his impeachment afterward were up for competitive races against targeted, Trump-endorsed opponents.

A front-runner in the Nevada GOP Senate primary, the state's former Attorney General Adam Laxalt, is a fervent Trump supporter. In 2020, he chaired Trump's reelection campaign in the state and supported Trump's effort to overturn the 2020 election.

Laxalt hails from a political dynasty. His grandfather Paul Laxalt served as a senator for Nevada and his father, Pete Domenici, was New Mexico's longest-serving senator.

Some of the issues Laxalt ran on included stronger southern border policies, protecting the Second Amendment and changing how elections are conducted -- echoing many other conservatives running at the local level who, like Trump, baselessly claim there is a widespread election fraud problem that needs to be addressed.

Laxalt not only secured an endorsement from Trump but from other 2024 presidential hopefuls, including Florida Gov. Ron DeSantis, former Secretary of State Mike Pompeo, Texas Sen. Ted Cruz and Arkansas Sen. Tom Cotton.

But Laxalt still faced some competition in the primary from Sam Brown, a veteran and businessman. Laxalt was also seen by some as too close to the Republican establishment.

While serving in Afghanistan as an ​​Army infantry lieutenant, Brown was wounded by a roadside bomb attack and was sent to Texas to recover from his severe burn injuries.

Democratic Sen. Catherine Cortez Masto did not face any serious challengers in her primary, but the general election will test her support within Nevada as voters grow frustrated with the first-termer over economic challenges in a tourist-driven state hit hard by the COVID-19 pandemic and subsequent fallout, including rising inflation.

Meanwhile, in the House, incumbent Democrats may have cause for worry in the general more than the primary. Their seats have been rated toss-ups by the Cook Political Report.

Most in danger is Rep. Dina Titus, who said she got "f-----" by the state legislature on how they drew her district.

As for Nevada's gubernatorial race, all eyes have been on the GOP primary, where Clark County Sheriff Joe Lombardo led the very crowded field. Lombardo -- who has plenty of name recognition around the state's most populated area, Las Vegas -- received an endorsement from Trump.

Nevada's governor race later this year could potentially be a referendum on incumbent Democrat Steve Sisolak, who has had a somewhat difficult first term. Sisolak had to navigate the onset of COVID, which caused Nevada's tourism-based economy to suffer.

Meanwhile, the GOP primary for secretary of state is drawing attention to Jim Marchant, the leading GOP candidate in the race, who has falsely claimed Trump won the 2020 election. Marchant's candidacy is an example of a national trend involving supporters of the "big lie" running for offices like secretary of state in order to influence how elections are conducted.

Marchant would most likely face Cisco Aguilar in November if he wins the primary.

On Tuesday in South Carolina, incumbent Republican Reps. Nancy Mace and Tim Rice had to contend with Trump's rage after denouncing him in the wake of the Jan. 6 attack.

They were up against Trump-endorsed opponents for races the former president has called "two of the most critical primary elections in the country."

Mace, the freshman congresswoman who just days into her term condemned Trump's claims about his election being stolen, was challenged by cybersecurity analyst and former state Rep. Katie Arrington, whom Trump called a "true Republican."

"I am trying to communicate to my colleagues in Congress that rhetoric has real consequences." Mace said on ABC News Live on Jan. 6, 2021.

"And in fact, when I came up for this weekend with my children for my swearing in, I actually put them on the first plane home on Monday morning because I was worried about what might happen today because of the rhetoric we've been hearing," she said then.

Mace, running in the state's 1st district seat, was endorsed by former Trump ambassador and two-term South Carolina Gov. Nikki Haley. Tuesday's primary put Haley -- a rumored 2024 presidential hopeful -- to the test against Trump. A third candidate on the ballot was Lynz Piper-Loomis.

In South Carolina's 7th Congressional District, state Rep. Russell Fry received the endorsement of Trump against five-term Rep. Rice, who has consistently defended his post-Jan. 6 impeachment vote and condemnation of Trump's role in the insurrection.

Rice's break with Trump is notable as his district has displayed staunch support for the former president: It voted for Trump by a 19-point margin in 2020.

The special election for Texas' 34th District seat has been a study in the kinds of races national Democrats and Republicans may deem as winnable -- all in a contest to serve just six months in an area carved up by redistricting anyway.

Voters there headed to the polls for a third time this election season to cast a ballot for a short-term representative; this race is separate from the one being decided in November's general election contest.

The messy electoral timeline was caused by former Rep. Filemon Vela's decision to resign in March in order to work in the private sector after the Democratic lawmaker had already announced he would not seek reelection.

The situation created a sped-up political calendar for candidates already in the running, while also offering Republicans the opportunity to flex their growing popularity in the heavily Latino area. Meanwhile, national GOP groups appeared to be going all-in on the possibility of upending Democrats' head start ahead of the general election, pouring money into the race.

National Democrats have largely steered clear of the special election.