House Republicans are promising to soldier on with their impeachment inquiry into President Biden despite a flagging case against the president, a conference divided on moving forward, and ambiguity as to whether impeachment has proved to be an effective political tool.

In a letter to Congressman James Comer, a special counsel to the president, Richard Sauber, told Mr. Comer that the impeachment investigation into Mr. Biden “is over.” 

“Your Committee’s purported ‘impeachment inquiry’ has succeeded only in turning up abundant evidence that, in fact, the President has done nothing wrong,” the letter, first reported by CNN, reads. “Yet rather than acknowledge this reality, your March 28, 2024, letter contains the same litany of false allegations that have been repeatedly debunked and refuted by the very witnesses you have called before your Committee and the many documents you have obtained.”

The letter follows a rough patch for GOP investigators, which began when the GOP’s star witness, Alexander Smirnov, was arrested for allegedly fabricating a story about Mr. Biden and his son Hunter Biden allegedly receiving bribes from a Ukrainian energy company.

Mr. Comer eventually responded to this critical blow to his case by saying he would make criminal referrals to the Justice Department and requesting that the president testify in front of his committee.

A representative from the House Oversight Committee tells the Sun that, despite the issues with the case for impeachment, “The impeachment inquiry is ongoing and impeachment is 100 percent still on the table.”

“The Committees will continue to investigate President Biden’s abuse of public office and will outline findings in a final report with recommendations,” the representative said.

Though the Oversight Committee still promises that a formal impeachment is on the table, it’s not clear that they have the votes to pass an impeachment resolution. The leadership of the GOP’s House campaign arm has also signaled it is de-emphasizing the effort.

One Republican on the Oversight Committee, Congresswoman Lisa McClain, told CNN last month that she didn’t think the inquiry would end in an impeachment vote. “I think the American people want outcomes. They want change. They want policy change,” Ms. McClain said. “So, do I think he is going to get impeached? No.”

Whether or not Republicans are able to muster the votes for a formal impeachment vote in the House, a Senate trial would likely be dismissed, as is expected to happen with the impeachment of the Secretary of Homeland Security, Alejandro Mayorkas.

However, the impeachment investigation and flurry of coverage of the claims made by Mr. Comer and other Republicans against the president may still have served its intended purpose if that purpose was more political than practical.

A Gallup survey released in early April found that fewer than half, or 46 percent, of Americans feel that Mr. Biden is trustworthy. For comparison, a September 2020 Gallup poll found that a majority, 52 percent, thought the then-candidate was trustworthy.

Gallup also reported that perceptions of President Trump as trustworthy declined to 28 percent among independent voters in 2024 from 31 percent of independents in 2020.

Between the 2020 Gallup survey and the 2024 Gallup survey, Mr. Biden’s perception as being trustworthy slid the most among independent voters. In 2020, the majority of independents, or 54 percent, saw Mr. Biden as trustworthy. In 2024, just 44 percent of independents reported seeing Mr. Biden as trustworthy.

Perceptions of Mr. Biden as trustworthy also declined among Democrats by 5 points and among Republicans by 3 points between the 2020 and 2024 surveys.

Similarly, an April Marquette University Law School poll found that some 47 percent of likely voters nationally see Mr. Biden as having behaved corruptly, compared to 63 percent who said the same of Mr. Trump.

While the pollster has only been asking about perceptions of corruption since September of 2023, the director of polling at Marquette Law School, Charles Franklin, tells the Sun that there has been “very little change for either” Mr. Biden or Mr. Trump over that time period.

When the pollster first started asking about perceptions of corruption, 45 percent of respondents said they thought Mr. Biden had behaved corruptly, while 63 percent said the same of Mr. Trump.

A political scientist at John Jay University, Brian Arbour, tells the Sun that he’s skeptical that the impeachment effort accomplished much for the Republicans politically — at least at this stage.

“Most people who say they want to impeach Biden would have said that on January 19th 2021 and most people who don’t would never say that no matter what he does,” Mr. Arbour says. “The impeachment itself — I don’t think is persuading any swing voters.”

Mr. Arbour adds, “Now the second-order effects on things like trustworthiness are a more fruitful place to look,” though he notes that a drop in perceived trustworthiness could be attributed to any number of issues.

The one area Mr. Arbour did think that the impeachment efforts may have been most useful for the GOP is in keeping their voters from leaving the GOP, which he says is “just a bigger issue with Trump.”