Wisconsin Sen. Tammy Baldwin and her Republican challenger, Eric Hovde.
CNN  — 

Wisconsin Republicans will nominate businessman Eric Hovde to take on Democratic Sen. Tammy Baldwin, CNN projects, in a contest seen as crucial to the battle for control of the narrowly divided Senate.

Both Hovde and Baldwin are projected to advance in their respective primaries Tuesday – with Hovde overcoming nominal opposition from two little-known candidates and Baldwin unopposed.

Their wins set up one of the year’s marquee Senate races, in a state that is also poised to be a major presidential battleground.

Recent polling has given Baldwin the edge in her quest for a third term. A New York Times/Sienna College poll from earlier this month found the senator leading Hovde 51% to 43% among registered voters.

Hovde, in Madison on Tuesday, acknowledged the surge of Democratic energy after Vice President Kamala Harris ascended to the top of the Democratic ticket once President Joe Biden stepped down – a change that could also damage the prospects of down-ballot Republicans.

But he said he believes this surge is “temporary.”

“I think everybody on the Democratic side was very depressed about realizing how bad Joe Biden was, from a mental capacity standpoint. So, of course, you’re going to get that kind of bump. But look, I feel there’s enormous amount of energy on the Republican side,” he said.

“This state has always been a purple state. As we all know, every election is very close, but those people in the middle that decide this election – I think they’re struggling, and over half of America feels like they’re in a recession,” Hovde said, predicting that voters would “break in a different direction.”

Baldwin had skipped Biden’s rally in Wisconsin after his disastrous late-June debate with former President Donald Trump. However, she attended and spoke at Harris’ July 23 event in Milwaukee – her first campaign rally as a presidential candidate this year.

“Wisconsin will likely decide who occupies the White House, and which party controls the United States Senate,” Baldwin said at the time, adding, “No pressure.”

Baldwin pointed to scheduling conflicts when asked Thursday about her choice to appear with Harris but not Biden.

With the general election matchup between Hovde and Baldwin looking all but certain for months, the ad battles began early.

Already, the race has seen nearly $66 million in ad spending, with Democrats outspending Republicans by about $40 million to $26 million. Baldwin leads all advertisers by a wide margin, having spent nearly $24 million, while the self-funding Hovde has spent about $15 million so far. Both candidates and their allies have used their ample airtime to run waves of attack ads, often featuring sharp personal criticism.

And reflecting the competitive nature of the race, the parties have a combined $48 million in future reservations – the seventh-most among all Senate races – with Democrats holding a significant edge in future bookings, $37 million to $10 million.

Baldwin’s ads have focused on her efforts to lower prescription drug costs and provide health care to veterans suffering from exposure to toxic burn pits. The senator and her allies, meanwhile, have also sought to brand Hovde as a carpetbagger – the Republican, who is the CEO of Sunwest Bank, bought a house in Laguna Beach, California, after losing an earlier bid for Senate in 2012.

And a recent Baldwin campaign ad seized on Hovde’s previous remarks attributing societal problems to children being born out of wedlock.

“That just shows Eric Hovde is ignorant,” one person says in the ad. “Come on. I’m successful today because of my mom,” another adds. “I learned my work ethic from my mom – my single mom,” a third person says. “What is wrong with this guy?” adds a fourth.

Hovde has looked to blunt the Democratic criticism by touting his connections to the state. “I’m a fourth generation Wisconsinite. It made me who I am,” he says in one ad.

Before the Democratic shake-up at the top of the ticket, Hovde ran ads trying to press Baldwin to say whether she thought Biden should step aside – which she did not. After Biden dropped out of the race, Hovde attacked the senator for not taking a firm enough stand, accusing her of being part of a “Biden cover-up.”

Hovde’s campaign recently launched a spot to coincide with the Olympics coverage, featuring footage of athletes training as Hovde ticks through a list of conservative priorities, while wearing a striking American flag-themed polo shirt.

“Our country has taken a beating the last few years, but I know we can turn it around. It’ll take a lot of hard work like these athletes put in. We need to get serious about our spending that has caused prices to skyrocket. We need to fix our health care and address the shortage of affordable housing. Also, we must close our border, stop the flow of fentanyl and put Americans first,” Hovde says in the spot.

CNN’s Simone Pathe contributed to this report.