5 Takeaways From Tuesday’s Key Primary Races

From Las Vegas to Lewiston, Maine, the contours of critical midterm contests came into focus on Tuesday as Americans voted in major federal and state races across five states.

In Nevada, which will be home to marquee House, Senate and governor’s races this fall, Republicans elevated several candidates who have embraced former President Donald J. Trump’s lies about a stolen election — even as candidates he endorsed had a mixed night in South Carolina, where he had sought to exact vengeance on two House incumbents.

In Maine, a familiar set of characters moved into highly competitive general election races for governor and for a House seat that may be one of the most hard-fought in the nation. But in Texas, Republicans flipped a Rio Grande Valley seat — albeit only through the end of the year — as the party works to make inroads with Hispanic voters.

Here are a few takeaways from Tuesday’s primaries:

Election deniers prevail in Nevada.

Republican candidates who have embraced Mr. Trump’s lies about election fraud were nominated for several positions of significant power in one of the most competitive political battlegrounds in the nation.

They include Jim Marchant, an organizer of a network of 2020 election deniers. Mr. Marchant, who prevailed in Nevada’s Republican primary for secretary of state, is also a failed congressional candidate who declared himself a “victim of election fraud” after being defeated in 2020, and has said his “No. 1 priority will be to overhaul the fraudulent election system in Nevada.”

Mr. Marchant was among an alternate slate of pro-Trump electors who sought to overturn President Biden’s victory in Nevada in 2020, and he has said he would have refused to certify the election had he been secretary of state at the time.

Adam Laxalt, Nevada’s former attorney general who won his party’s Senate nomination on Tuesday with Mr. Trump’s backing, was one of the leaders of the Trump campaign’s effort to overturn the results in Nevada.

And in the Republican primary to challenge Representative Steven Horsford, a Democrat, the two top finishers with 40 percent of the vote counted, according to The Associated Press, were Annie Black, a state lawmaker who said she was outside the Capitol on Jan. 6, 2021, and Sam Peters, who has suggested he would not have voted to certify the 2020 election results and questioned the legitimacy of Mr. Biden’s victory.

Their victories come as a bipartisan House panel investigating the Jan. 6, 2021, attack on the Capitol has showcased testimony from Mr. Trump’s onetime top advisers discussing Mr. Trump’s claims.

“He’s become detached from reality if he really believes this stuff,” William P. Barr, the former attorney general, told the panel.

Critical Nevada races come into focus.

Nevada cemented its status as a focal point of the political universe on Tuesday, as several marquee general election contests took shape that will have significant implications for the balance of power in Washington.

Senator Catherine Cortez Masto, a Democrat, will face off against Mr. Laxalt, who comes from a prominent political family. His positions on issues like election integrity may run afoul of some voters in a state that hasn’t supported a Republican for president since 2004.

But Ms. Cortez Masto may be the Senate’s most vulnerable Democratic incumbent. And there are signs that Nevada, which currently has among the highest gas prices in the nation, may be notably difficult terrain for Democrats this year, as they grapple with a brutally challenging political environment shaped by issues including soaring inflation and President Biden’s weak approval rating.

Those dynamics will also influence the governor’s race, as Gov. Steve Sisolak prepares for a challenge from Joe Lombardo, the Clark County sheriff. And all three of the state’s incumbent Democratic House members are running in highly competitive seats.

South Carolina shows the power, and some limits, of a Trump endorsement.

After the Jan. 6 attack on the Capitol, two House members from South Carolina broke with most of their fellow Republicans to lash Mr. Trump as complicit in the assault. On Tuesday, only one of them prevailed over a Trump-backed primary challenger.

Representative Nancy Mace, who’d said she held Mr. Trump “accountable for the events that transpired, for the attack on our Capitol,” defeated her challenger, Katie Arrington, a former state lawmaker. But Representative Tom Rice, who stunned many observers with his vote to impeach Mr. Trump, lost to State Representative Russell Fry as he campaigned in a more conservative district.

A Trump endorsement is not always dispositive, as other primary election results this year have demonstrated. But the former president’s continued sway over the Republican base is undeniable. And openly challenging him remains politically dangerous for Republican candidates, as several who voted to impeach him have experienced.

Despite her initial sharp criticism of Mr. Trump, Ms. Mace — who did not vote to impeach — went on to make overtures to Trump loyalists, including by issuing an appeal from outside Trump Tower as part of her broader campaign pitch.

Mr. Rice, by contrast, appeared to grow sharper in his condemnations of the former president in the final stretch of the race.

“It’s not about my voting record. It’s not about my support of Trump. It’s not about my ideology. It’s not because this other guy’s any good,” Mr. Rice said. “There’s only one reason why he’s doing this. And it’s just for revenge.”

Making that argument proved fruitless for Mr. Rice. On Tuesday, he became the first Republican who voted for impeachment to be defeated in a primary.

Republicans win in the Rio Grande Valley and call it a bellwether.

Republicans are seeking to make inroads with Hispanic voters this year after doing far better than expected in parts of South Texas in 2020 — and they immediately moved to cast a special election victory in the Rio Grande Valley on Tuesday as a bellwether for the region.

Mayra Flores, a well-funded conservative, won a seat vacated by former Representative Filemon Vela, a Democrat, who resigned earlier this year. Ms. Flores avoided a runoff that some had expected, and her fund-raising vastly exceeded that of her closest Democratic competitor, Dan Sanchez.

She will be the first Republican from the district and the first Latina Republican from Texas in Congress.

But a November election will decide who represents the district for a full two-year term that starts in January. Ms. Flores will face Representative Vicente Gonzalez, a Democrat who currently represents a neighboring district. The district has been redrawn for the general election to be overwhelmingly Democratic, and Mr. Gonzalez is favored to win.

Democrats also say they have been more focused on other races that they expect to be more competitive in the general election.

But Republicans were quick to highlight what they saw as larger meaning in Ms. Flores’s win.

“Mayra has sent a resounding message to the Democratic Party in South Texas and across America — Democrats do not own the Hispanic vote,” said Representative Elise Stefanik of New York, whose political action committee endorsed Ms. Flores.

Ms. Flores cast her race as one with national and even heavenly implications. “Today is the day that we can make history together and jump start the great red Godly wave!” she declared.

In a Maine House rematch, shifting political winds spell trouble for Jared Golden.

Representative Jared Golden of Maine is the rare Democrat to represent a district Mr. Trump won. Former Representative Bruce Poliquin, a Republican whom Mr. Golden narrowly defeated in 2018, will now work urgently to change that.

Mr. Poliquin, who easily prevailed in his primary on Tuesday, heads into a rematch against Mr. Golden in a sharply different political environment from during their last contest, when backlash against Mr. Trump fueled a Democratic takeover of the House of Representatives.

This time around, Democrats are the ones facing staggering political headwinds.

Mr. Golden, a Marine veteran who fought in Iraq and Afghanistan, has broken frequently with the national party — just last week he voted with Republicans against some Democratic gun control measures — and the race for Maine’s Second Congressional District is now poised to test how much independent personal brands can help candidates outrun a brutally challenging political climate.

Maine’s race for governor is also expected to be tightly contested. On Tuesday, former Gov. Paul LePage — a bombastic Republican — became his party’s nominee. He will run against Gov. Janet Mills, a Democrat.