When the GOP eked out its microscopic House majority, the joy in the Republican cloakroom had little to do with passing major bipartisan legislation. What the House Republicans gained was the second-biggest lever of the legislative branch — the power to probe.

Exuberant members of what might be dubbed the “Fox News Nation” imagined the White House begging for mercy after a relentless House investigation into Hunter Biden and his infamous laptop.

In this fantasy, technology companies would be forced to admit they deliberately rigged their algorithms to guarantee Joe Biden’s victory in the 2020 presidential election. And Democratic heroes like Dr. Anthony Fauci would wilt under withering cross-examination about mask mandates and the origins of COVID-19.

That was the theory, anyway. But this is the week when the gavel hits the podium, as House Republicans begin to confront the political limits of heavy-handed congressional hearings.

Tuesday night, in prime time, the House select committee on China will hold its first hearing with hawkish former national security officials from the Trump administration opining from the witness table.

Virtually every House committee — with the possible exception of Ethics — is poised to weigh in on the East Palestine, Ohio, train derailment.

Jim Jordan, the incendiary chairman of a new Judiciary subcommittee on the so-called weaponization of the federal government, has subpoenaed Attorney General Merrick B. Garland and FBI Director Christopher Wray as part of his investigation into the alleged targeting of parents during 2021 school board protests.

Meanwhile, James R. Comer, who chairs the House Oversight and Accountability Committee, is going after the finances of the Biden family — especially Hunter — as well as probing the botched 2021 American withdrawal from Afghanistan.

On the surface, it sounds devastating for Biden and his fellow Democrats. But, in all likelihood, the overwrought House hearings will make little difference when Americans vote for president and control of Congress in 2024.

Persuasive congressional hearings require a veneer of fairness.

The Senate Watergate hearings in 1973 were devastating to Richard Nixon because Select Committee on Presidential Campaign Activities Chairman Sam Ervin, D-N.C., excelled at creating the aura that he was a simple country lawyer only interested in the truth.

There were no Trump supporters on the House Jan. 6 select committee that looked into the 2021 Capitol riot, but the nine members — seven Democrats plus Republicans Liz Cheney of Wyoming and Adam Kinzinger of Illinois — were careful to avoid bombast as they tried to let the evidence speak for itself.

While there may be exceptions, most House Republicans who will be orchestrating the hearings into Biden land possess, shall we say, less than a judicial temperament.

In their partisan zeal, they are reminiscent of the despotic Queen of Hearts in “Alice’s Adventures in Wonderland,” who decreed: “Sentence first — verdict afterwards.”

Making shrill charges and angrily hectoring Democratic witnesses is a guaranteed tactic to get clips from a House hearing featured on Fox News. But it is also a self-defeating attempt at winning the trust of swing voters.

A recent polling analysis by Amelia Thomson-DeVeaux of FiveThirtyEight found that “Americans don’t seem to have much of an appetite for a slew of public hearings — at least, not the ones that Republicans have planned.”

An emblematic late January poll by the Pew Research Center found that 65 percent of Americans worry House Republicans will focus “too much” on investigating the Biden administration. Even 42 percent of Republicans and those who lean toward the GOP feel that way.

In right-wing media circles, the unquestionably sleazy business dealings of Hunter Biden are ballyhooed as the worst scandal since Benedict Arnold defected to the British.

Scandals to nowhere

The problem for House Republicans is that there is little historical evidence that an incumbent president is politically damaged by anything that occurred before he was inaugurated. The logic is simple: Any incumbent president does enough in office to arouse partisan opposition without having to delve into ancient history.

During former President Bill Clinton’s first term, endless effort was spent investigating a penny-ante failed Arkansas real estate deal called Whitewater. While it did lead to the appointment of Kenneth Starr as independent counsel, Whitewater played little to no role in Clinton’s 1996 reelection campaign.

A September 2004 furor over a faulty “60 Minutes” story about George W. Bush’s Vietnam-era service in the Air National Guard led to the ouster of four CBS News employees and hastened the retirement of anchor Dan Rather. But in the midst of the 2003 Iraq War, voters had little interest in what the incumbent president was doing during another war more than 30 years earlier.

When Trump ran for reelection in 2020, the “Access Hollywood” tape was barely mentioned. Democrats and so-called never Trumpers had so many other valid reasons to oppose the incumbent’s reelection without resurrecting his crude sexual bragging from 2005.

None of this is designed to downplay the significance of the China hearings and the developing House investigations into a frightening railroad derailment.

But, if done right, these hearings will not just trot out a cardboard cast of prefabricated villains. Whether the topic is China or railroad safety, the American business community may face far more devastating scrutiny than the Biden administration.

In their 2017 book, “Investigating the President,” political scientists Douglas Kriner and Eric Schickler noted: “For an investigation to affect public opinion and impose political costs on the president, it must receive enough coverage in an increasingly partisan media environment to reach a wide swath of voters.”

That is the unbridgeable dilemma for House Republicans. The more that the Republicans play to their political base, the more they fulminate and fume, the more likely their Biden probes will be dismissed as a political circus by independent voters.

Actually, a circus has trapeze artists and jugglers. The GOP hearings will only offer rage and retribution.

Walter Shapiro has covered the last 11 presidential campaigns. He is also a fellow at the Brennan Center for Justice at NYU and a lecturer in political science at Yale. Follow him on Twitter @MrWalterShapiro.