At the beginning of the year, President Trump had a clear advantage over Democrats on the issue of corruption. Voters saw him as too wealthy to be bought or bossed, an outsider intent on “draining the swamp.” But that advantage has diminished. In the wake of this week’s conviction and guilty plea of Mr. Trump’s former campaign chairman and personal attorney, Democrats are now decrying the “cesspool of self-enrichment, secret money and ethical blindness” of Republican-controlled Washington, as House minority leader Nancy Pelosi put it on Tuesday. That includes the indictments of Rep. Duncan Hunter (R) of California on campaign finance abuses and Rep. Chris Collins (R) of New York for insider stock trading. Opinions about Trump are so hardened that it may only have a minimal impact on the upcoming midterm elections. But in divided America, elections are often won on the margins. And among “reluctant” Republicans – those who backed Trump in 2016 largely because they didn’t like Hillary Clinton – a “culture of corruption” message could have an impact. “They’re not a majority, but they are more than enough to tip a lot of these close elections,” says John Pitney, a political science professor at Claremont McKenna College in Claremont, Calif.

Opinions about President Trump are so hardened that this week’s bombshell conviction and guilty plea of his former campaign chairman and personal attorney may only have a minimal impact on the upcoming midterm elections.

But in divided America, elections are won on the margins – and that is where this week’s news, along with the indictment of Rep. Duncan Hunter (R) of California, could move the needle. In swing districts, particularly among “reluctant” Republicans, a “culture of corruption” message could influence voters, though Democrats are being very careful as to how they craft that message.

“The best thing that Trump has going for him right now is the polarization of the electorate. Probably most Republicans are sticking with him,” says John Pitney, a political science professor at Claremont McKenna College in Claremont, Calif. But this week’s developments could sway those voters who backed Mr. Trump in 2016 largely because they didn’t like Hillary Clinton, he says. “They’re not a majority, but they are more than enough to tip a lot of these close elections.”

Corruption is seldom a top issue for voters, says Mr. Pitney. It’s usually the economy, and that’s one thing that Republicans have in their favor. “But corruption can matter if people hear enough about it.”

That happened in 1994, when Rep. Newt Gingrich (R) of Georgia led a Republican takeover of the House for the first time in 40 years. He had a policy agenda, the “Contract with America,” but he also hammered home various scandals among House Democrats.

The scandal strategy backfired, though, when House Republicans moved to impeach President Bill Clinton in 1998. Many voters viewed it as overreach for a president’s personal indiscretions, even though Mr. Clinton later admitted to making false statements. The move cost Republicans four seats in that year’s midterms, and Speaker Gingrich resigned – under an ethics cloud of his own.

“That was a complete flop of an effort – and of course, Newt Gingrich paid the price,” says former House historian Ray Smock.

It is not surprising then, that Democratic leaders are laying off the “i” word – impeachment – despite tremendous pressure from progressives and big-money Democrats such as Tom Steyer.

“It’s not a priority,” House minority leader Nancy Pelosi (D) of California told the Associated Press after former Trump campaign manager Paul Manafort was convicted Tuesday of bank and tax fraud and Michael Cohen, the president’s former attorney and “fixer,” pleaded guilty to bank and tax fraud charges as well as campaign finance violations.

Mr. Cohen directly implicated Trump as having ordered him to pay two women during the 2016 campaign to silence them about their alleged affairs with Trump. The president is now an “unindicted co-conspirator,” said Senate minority leader Charles Schumer (D) of New York on Wednesday, demanding that the Senate Judiciary Committee immediately pause consideration of the president’s US Supreme Court Nominee, Judge Brett Kavanaugh – to no avail.

Senator Schumer, too, waves off impeachment talk. For one thing, Democrats fear it will energize the Republican base. For another, they want the special counsel, Robert Mueller, to finish his work and report on Russian interference with the 2016 election and whether there was any collusion with the Trump campaign.

They are more than happy, however, to point to the “cesspool of self-enrichment, secret money and ethical blindness” of Republican-controlled Washington, as leader Pelosi put it in a statement Tuesday. That includes the indictments of Congressman Hunter on campaign finance abuses and Rep. Chris Collins (R) of New York for insider stock trading.

Both men were Trump’s very first congressional endorsers, and while Congressman Collins now says he will not seek reelection, a defiant Hunter is barreling ahead. He’s blasting a Justice Department “witch hunt” and media coverage for his troubles. He and his wife face dozens of criminal charges for misusing more than $250,000 in campaign funds on everything from European vacations to the water bill. Speaker Paul Ryan has stripped him of his committee assignments.

In a Trump-friendly Midwestern district, such as the one that Rep. Cheri Bustos (D) of Illinois handily won in 2016, “we can't just be running on an anti-Trump message, even with everything that happened” this week, says Congresswoman Bustos. What Democrats should do, she says, is continue to emphasize kitchen-table issues, like healthcare costs and low wages, while also pointing out the Republicans’ failure to exercise proper oversight of the administration.

“You barely hear a peep out of them. They are literally rubber-stamping corruption,” she says.

Of course, Democrats are not scandal-free. A new Quinnipiac poll shows incumbent Sen. Robert Menendez (D) of New Jersey suddenly in a horse race now that the Senate ethics panel has “severely admonished” him. In January, the Justice Department dropped bribery and other charges against him after a mistrial. The poll finds that ethics is the number one issue in deciding how New Jersey voters will cast their ballot for US Senate.

Still, acting as a “check and balance” on the president is emerging as a powerful campaign theme, particularly among suburban women, where support for Trump is eroding, says Democratic pollster Celinda Lake. This week’s news about Manafort and Cohen is likely to help outsider and female candidates, whom voters tend to see as “more honest.”

At the beginning of the year, it was the president who had the advantage over Democrats on corruption, says Ms. Lake. Among independents, he had as much as a 24-point lead, her polling showed. Voters saw him as too wealthy to be bought or bossed, an outsider intent on “draining the swamp.” But that advantage has diminished, she says.

Kyle Kondik, managing editor of the independent Sabato’s Crystal Ball political forecast, points out that Tuesday’s double-whammy against two former stars of Trump’s inner circle will probably not affect the president’s approval ratings. But that doesn’t mean it won’t matter in the battle for the House, because views of Trump are hardened in a way that is “poor for the president, and for his fellow Republicans.”

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Trump’s ratings are “stuck” in the low-to-mid 40s, he writes, and this week’s news won’t raise them. A threat of impeachment could possibly rally Trump’s core supporters, but Trump and Republicans have a bigger problem than motivating the base, and that is a “persuasion problem with soft Republicans in the suburbs” who don’t like him.

If the political environment is favoring House Democrats, Republicans need something positive to improve Trump’s numbers, says Mr. Kondik in an interview. “This is not that.”