Democratic voters in Nebraska will decide on their candidate in a key battleground House district on Tuesday, as the party seeks to stoke optimism about regaining control of Congress this fall despite recent redistricting setbacks that have left them feeling glum.

Democrats in the state will also weigh in on a bizarre Senate primary where they hope a political bank shot will ultimately oust a Republican incumbent — an uphill battle in the deep-red state that could turn on rural voters’ anxieties over agricultural tariffs and the economy.

In West Virginia, a Republican governor will test whether he has the clout to push out members of his own party in the State Legislature who he says don’t meet his standard.

Here’s what to watch for on Tuesday evening in Nebraska and West Virginia:

Do shenanigans in Nebraska help or hurt Dan Osborn?

Dan Osborn, a former labor leader who ran unsuccessfully for Senate in 2024, is back this year, running as an independent against Senator Pete Ricketts, a Republican. Democrats have thrown their support behind him and see a faint — but not impossible — chance of ousting a Republican in a conservative state that has felt the effect of President Trump’s tariffs.

To give Mr. Osborn a clean shot at Mr. Ricketts, the Nebraska Democratic Party had hoped to keep the ballot clear of any Democratic candidate who could split the left-leaning votes Mr. Osborn is likely to attract.

But there is a Democratic primary on Tuesday, between William Forbes, a pastor who has voted for Mr. Trump and is accused of being a Republican “plant” in the race, and Cindy Burbank, a retiree who has said she plans to drop out of the primary after winning to clear the field for Mr. Osborn. Democrats have tried to educate their voters about the unusual dynamics of the race and urged them not to back Mr. Forbes.

Who emerges from the ‘blue dot’ primary?

Representative Don Bacon, a moderate Nebraska Republican and a frequent critic of Mr. Trump, is not running for re-election, leaving his battleground district in Omaha an appealing target for Democrats.

Three candidates have led the crowded field: John Cavanaugh, a state senator; Denise Powell, a political organizer; and Crystal Rhoades, a court clerk.

Brinker Harding, an Omaha city councilman and a friend of Mr. Bacon’s who has inherited much of his campaign team, is running unopposed in the Republican primary.

Among the Democrats, Mr. Cavanaugh faces an unusual political argument from his rivals: Electing Mr. Cavanaugh, they say, could imperil the chances that a Democratic presidential candidate will win the White House in 2028.

Their rationale stems from a quirk in how Nebraska allocates its electoral votes. Aside from the two votes a presidential candidate gets in a statewide victory, an additional vote is awarded to the winner of each of its three congressional districts. The single vote in the Omaha district, which could make a difference in a close election, is often won by a Democrat, even while the rest of the state goes to the Republican.

Mr. Cavanaugh’s opponents say they fear that if he wins, the loss of his vote in the State Legislature could make it easier for Republicans there to vote to abolish the so-called blue dot system — named for the speck of blue on the electoral map that shows the Omaha district in a sea of red — which they have already tried to do. Mr. Cavanaugh has responded that the system is not in peril and that other Democrats are likely to be elected to the Legislature in his stead.

Do incumbents get their way?

A handful of incumbent Republicans face primary challengers who are not expected to threaten their careers but could determine the strength of their support among voters. That group includes Mr. Ricketts, Senator Shelley Moore Capito of West Virginia and Gov. Jim Pillen of Nebraska.

West Virginia’s contest will also be a test of Gov. Patrick Morrisey’s ability to exact Trump-like retribution on political adversaries. Mr. Morrisey has endorsed a number of Republican primary challengers to incumbents in the State Legislature as he attempts to reshape the G.O.P. supermajority and impose his political will after several contentious legislative sessions.

“I’m willing to go in if there’s a superior candidate,” Mr. Morrisey told reporters last week, referring to wading into Republican primaries. “We cannot settle for second best.”