Over the course of the impeachment inquiry, the GOP’s primary defense of President Trump—that he was right to want an investigation into Joe Biden and son—has taken on a life of its own.

For months, the president’s advocates have alleged that Biden, as vice president, corruptly endeavored to protect his son Hunter’s business dealings in Ukraine—meaning that Trump’s push for Ukrainian President Volodymyr Zelensky to open an investigation would have been not self-serving but justified. The Bidens have denied wrongdoing. Neither U.S. nor Ukrainian officials ever filed criminal charges, and the former Ukrainian prosecutor general, Yuriy Lutsenko, said in May 2019 there was no evidence of wrongdoing by the Bidens.

Now, with the Senate on the eve of a vote to acquit Trump on charges that he abused his power by withholding U.S. aid to Ukraine to secure that investigation, the Biden corruption counter-case has transformed into a core concern for the president’s base of supporters—many of whom now want to see the GOP-controlled Senate use its power to “get to the bottom” of it when the impeachment trial is over.

On Sunday, Sen. Lindsey Graham (R-S.C.) appeared on Maria Bartiromo’s Fox News show and vowed to use his authority—he’s chairman of the Senate Judiciary Committee—to do just that. “You should expect us to do this,” Graham told her viewers. “If we don’t do it, we’re letting you down.”

Bartiromo agreed. “They want accountability,” she told Graham. “For three years, this country has been in hysterics over collusion that never existed… We’ll be watching.”

The warning was clear as could be. The problem, however, is that on Capitol Hill, the appetite for a sweeping probe into the Bidens and Burisma appears limited—even among staunch defenders of the president.

“I think we should all hold hands in a big circle, sing Kumbaya, and quit all the stupid investigations,” said Sen. Rand Paul (R-KY) as he left the Senate floor on Monday. “We can do these endless recriminations forever and ever if we want… I think people are tired of the damn impeachment. Why can't we start talking about some things we could do to help the country, you know?”

Others evinced a similar desire to move on. Sen. James Lankford (R-OK) told The Daily Beast GOP senators have legitimate questions about the Biden and Ukraine matter. “I don’t think,” Lankford added, “there should be a tremendous, long-term protracted something unless something is there.”

“ I think people are tired of the damn impeachment. Why can't we start talking about some things we could do to help the country, you know? ” — Rand Paul

There also appears to be limited interest in a Senate investigation into the whistleblower complaint that sparked the impeachment inquiry, another core concern for the president’s base.

The path ahead for the Senate GOP, then, is fraught: after a hard-won fight to defeat Trump’s impeachment, they will have to balance ramped-up pressure from an aggrieved GOP base, hungry for revenge, with weary senators’ desire to leave everything Ukraine behind.

Graham isn’t totally alone in pushing for Biden investigations, however. Sen. Ted Cruz (R-TX) told reporters on Monday that he also wants to see Senate committees take them up once the impeachment trial has concluded.

“I will confess, prior to the impeachment trial I did not know the full scope of the evidence of potential corruption concerning Joe Biden,” said Cruz. “But the reason the President was particularly justified in asking for this investigation is, if you have corruption that goes to the very highest levels of government, that is a serious public concern.”

Cruz said he understood colleagues’ reservations about continuing to probe. “There’s no doubt we’re in the middle of an election, and the American people should decide,” he said. “But I can tell you, people are deeply frustrated because there doesn’t seem to be any accountability for corruption, or criminal misdeeds.”

The evidence of potential wrongdoing or criminality, however, is thin. It relies heavily on the shady imagery of Biden’s son serving on the board of Burisma, a company connected to Ukrainian figures with histories of corruption, while his father served as vice president of the United States. Republicans have pointed to contemporaneous emails sent to the State Department by Chris Heinz, stepson of former Secretary of State John Kerry and a onetime Hunter Biden business partner, relaying concern at the arrangement. The younger Biden has since acknowledged it was “poor judgment” to get involved in Ukraine.

As veep, Biden was a point person for the Obama administration on Russia and eastern Europe issues and in 2015, he pushed for the firing of a Ukrainian prosecutor, Viktor Shokin—even threatening to withhold U.S. aid until Shokin was gone.

GOP defenders of the president point to that as the real quid-pro-quo and allege that Biden wanted Shokin gone because he was investigating Burisma. But Ukrainian officials have said that the investigation was dormant at the time, and what’s more, a broad spectrum of U.S. and international officials, including Biden, were explicit about wanting Shokin gone because he was not seen as sufficiently anti-corruption.

During the Senate trial, the president’s defense team spent hours airing the Biden allegations. Some lawmakers, like Sen. Joni Ernst (R-IA), publicly speculated that they were actively damaging to Biden’s reputation and hurting his standing in the Democratic presidential primary. And Sen. Rick Scott (R-FL) took the step of running TV ads in the early caucus state of Iowa in which he declared that Biden “got away with it.”

To Democrats, who have argued that the trial provided the Biden-smearing spectacle that Trump wanted all along, the idea that congressional Republicans would move to investigate this further is farcical.

“If they want to deepen the view they have participated in a sham,” said Sen. Tim Kaine (D-VA), “they’re welcome to.”

Several Senate committees could carry out Biden-related investigations: Graham’s Judiciary Committee could look into it, as could the Senate Foreign Relations Committee, which is chaired by Sen. James Risch (R-ID).

Indeed, during his interview with Bartiromo, Graham made a personal appeal to Risch: “Jim, if you’re watching the show, I hope you are, we need to call the chief of staff to John Kerry, who was told about the conflict of interest with Hunter Biden being on Burisma’s board early on.”

A spokesperson for Risch said that the chairman hadn’t seen the interview and isn’t commenting on any investigations at this time.

A member of the Foreign Relations Committee, Sen. Marco Rubio (R-FL), quipped his panel would “probably have to fight Lindsey Graham” for jurisdiction. But he ultimately expressed a mainstream view among the Senate GOP: “I don’t think there can be any doubt that the arrangement that Vice President Biden’s son had is one that, under any other circumstances, people would ask questions about,” Rubio told The Daily Beast.

“Our ongoing concern,” he added, “should be whether we are sending a lot of money to a country that has serious corruption problems.”

On the other avenue of investigation that Trump and his supporters are craving—the whistleblower who they believed acted to deliberately undermine his presidency—progress appears unlikely.

Graham said that the chair of the Senate Intelligence Committee, Sen. Richard Burr (R-N.C.), would be moving shortly to have the whistleblower appear for testimony. But Graham, according to a knowledgeable Senate intelligence committee source, misrepresented the panel’s intentions toward the Ukraine whistleblower.

According to this source, there has been internal talk about inviting testimony from the whistleblower, a CIA official. But the focus of that testimony won’t be Ukraine or Trump. It’ll be strengthening whistleblower protections across the intelligence agencies—something the right-wing campaign to out the whistleblower has jeopardized.

Such testimony is unlikely to happen in the near future. The committee is in something of a holding pattern until the panel can “guarantee his or her safety, which has been the issue up till now,” the knowledgeable committee source said.

When asked if his committee would be moving to hear testimony from the whistleblower, Burr told reporters simply, “we’re investigating the whole whistleblower process.”

Even Paul, who has sought to draw attention to the whistleblower—even attempting to read aloud the name of someone alleged in conservative media to be that person—declined to urge Burr to investigate it further, simply saying the committee would have to decide.

If anything, Paul declared that it would be Democrats who would most aggressively take up the mantle of post-acquittal investigations, predicting that House Democrats would move to subpoena former national security adviser John Bolton within days.

“They’re the ones,” Paul said, “that aren’t going to let go of it.”

—with additional reporting from Spencer Ackerman