Polling commissioned in late May by the National Republican Senatorial Committee found Gallagher trailing Baldwin by 1 point — 46 percent to 47 percent, with 7 percent undecided.

Gallagher has met with the NRSC and has not closed the door on a bid, according to two people familiar with the discussions, and he is aware of the polling. A 39-year-old Marine veteran with degrees from Princeton and Georgetown, he played a large role in crafting cybersecurity policy in the 2020 defense spending bill. He has developed a reputation as a China hawk and leads the China Select Committee.

Sen. Steve Daines (R-Mont.), the NRSC chair, has led the full-court press. He has frequently praised Gallagher as a top-tier contender.

“Mike Gallagher would be a great candidate,” he told POLITICO in March. “He’s the kind of candidate that with his distinguished service and then time in Congress, could win both the primary and general election.”

The representative has not revealed which way he is leaning, saying only that he is focused on his work in Congress, specifically investigating the Chinese Communist Party. But he understands that Wisconsin is an important battleground and is hearing out those encouraging him to run, according to one of the people familiar with the discussions, who was granted anonymity because he was not authorized to discuss the lawmaker’s thinking.

The Senate GOP strategy in 2024 is centered on ousting incumbent Democrats in the red states of West Virginia, Montana and Ohio. But to widen the path to a majority, party strategists hope to contest several other Democratic-held seats in states that President Joe Biden carried narrowly. Wisconsin, which Biden won by less than 1 point in 2020, is one of those states.

Part of what makes Gallagher an appealing candidate is that he has not shied away from criticizing former President Donald Trump. He broke with the president over the Jan. 6, 2021, attack on the Capitol and earlier this year affirmed that he would not support Trump in 2024. Trump carried the state narrowly in 2016.

“I said two years ago that he lost my support,” Gallagher said in a March 2023 PBS interview. “I’m not going to change that.”

Besides Gallagher, Rep. Tom Tiffany (R-Wis.) and business people Eric Hovde and Scott Mayer are among those considering runs. But the NRSC has expressed a clear preference for Gallagher.

The poll the committee commissioned was conducted May 23-25 by Fabrizio, Lee & Associates, a firm that worked on the reelection campaign of Sen. Ron Johnson (R-Wis.) in 2022. Johnson narrowly beat Democrat Mandela Barnes. The pollsters surveyed 500 likely general election voters in Wisconsin; the results have a margin of sampling error of plus or minus 4.4 percentage points.

Other interesting data from the survey: Gallagher has relatively low name ID — 43 percent of the poll’s respondents had not heard of him. But his favorability is above water at 19 percent, with 9 percent viewing him unfavorably. Baldwin’s is right side up as well, at 43/38. But 43 percent of voters surveyed said they would not or probably would not vote to reelect her to a third term, while 40 percent said they would or probably would.

A generic Republican beat a generic Democrat by 4 points, 46 to 42 percent, in the survey.

Baldwin was first elected in 2012, beating former Wisconsin Gov. Tommy Thompson with 51 percent of the vote. Six years later she sailed to another term, besting state Sen. Leah Vukmir by 10 points.

The two could be somewhat evenly matched financially. Baldwin had $3.9 million on hand by the end of March. Gallagher had $3.3 million.