Key races to watch in June 4 primary elections in New Jersey, DC, Montana, South Dakota, New Mexico

Voters in New Jersey, South Dakota, New Mexico, Montana and Washington, D.C., will cast ballots in presidential and down-ballot primary elections on Tuesday.

These are some of the last primary elections and caucuses of the 2024 cycle.

But with President Joe Biden and former President Donald Trump the presumptive nominees of their respective parties, the most significant races to watch will be Senate primary contests in New Jersey and Montana, as well as a House race in New Jersey with a familiar family name mired in scandal.

Here are some of the key things to watch in the June 4 primaries:

Montana's Senate primary

In Montana, Senate primary elections will take place ahead of what is expected to be one of the upper chamber's marquee races that could determine the balance of power in the Senate come November.

Incumbent Sen. Jon Tester is one of two red-state senators aiming to hold onto their seats in places where Trump won the presidency in 2020. Tester is running against long-shot candidate, Navy veteran Michael Hummert in the Democratic primary.

On the GOP side, Tim Sheehy is expected to earn the nomination against former Montana Secretary of State Brad Johnson and environmental contractor Charles Walking Child. Sheehy will not compete against Republican U.S. Rep. Matt Rosendale, the GOP Senate nominee in 2018, who dropped out in March, less than a week after his entrance.

New Jersey's Democratic Senate primary

In New Jersey, the Democratic primary initially appeared action packed, as Rep. Andy Kim entered the race to take on indicted Sen. Bob Menendez -- followed by the state's First Lady Tammy Murphy, who initially consolidated most Democratic support behind her.

When Murphy dropped out, Kim became the frontrunner and was seen as on a glide path to the Senate, but Menendez on Monday filed to run as an independent, which could alter the race in the fall.

Menendez's entry as an independent will likely siphon votes from the Democratic nominee in the November general election, giving Republicans the glimmer of an opportunity to flip a seat Democrats must win to hold the Senate.

Menendez is the subject of an ongoing corruption trial, where he is accused of accepting cash, gold bars, luxury wristwatches and other perks from New Jersey businessmen in exchange for official favors to benefit the businessmen and the governments of Egypt and Qatar. Menedez has denied all wrongdoing and previously called the prosecution "overzealous."

If Kim wins the race in November, he would be the first Korean American elected to the U.S. Senate.

New Jersey's 8th congressional district race

In New Jersey's heavily Democratic 8th congressional district, another Menendez faces a tough fight to keep his seat.

On Tuesday, Democratic voters will select their nominee -- and, almost certainly, the district's next representative -- in a primary that pits first-term Rep. Robert Menendez Jr. against two challengers. Robert Menendez's serious threat comes from Ravi Bhalla, a civil rights lawyer and two-term mayor of Hoboken, a modestly-sized but influential commuter city across the Hudson from Manhattan.

All eyes will be on if the elder Menendez's independent bid weakens his son's position in what appears to be a close race.

As Sen. Menendez faces criminal corruption charges, Bhalla has attacked the younger Menendez as a beneficiary of nepotism from the state's influential Democratic party.

Also running in the Democratic primary is businessman Kyle Jasey.

First election after Trump's conviction

Tuesday's elections are the first since Trump's guilty verdict on all 34 counts in his hush-money trial -- although many votes were cast early or by mail before the jury's decision last week.

While a recent ABC News/Ipsos poll shows half of Americans, 50%, think former Trump's guilty verdict was correct, Tuesday will be the first time people respond with their ballots.

A Haley 'protest vote?'

On Tuesday, withdrawn GOP candidate Nikki Haley will be on the Republican presidential primary ballot in New Mexico. Haley will not be on the ballot in New Jersey and Montana. D.C. had its Republican presidential primary in March, which Haley notably won. South Dakota will not have a Republican presidential primary.

Haley has often received a decent percentage of vote in some presidential primaries even since dropping out, although in some states she may have received early votes or voting by mail.

It may be notable how Haley performs in New Mexico given that this is the first election after Trump's guilty verdict in his hush-money trial. Still, much of the vote she gets will likely be early vote or voting by mail cast before the verdict.

Recently, she received a large percentage of the vote in the Republican primary in Indiana (22%), Maryland (21%), Washington (19%), Nebraska (18%) and Arizona (18%).

Editor's note: This story has been updated to reflect that South Dakota will not have a Republican presidential primary.