House Republicans are doubling down in their effort to bring perjury charges against Hillary Clinton Hillary Diane Rodham ClintonBiden leads Trump by 36 points nationally among Latinos: poll Democratic super PAC to hit Trump in battleground states over coronavirus deaths Battle lines drawn on precedent in Supreme Court fight MORE over her testimony last year to the House Select Committee on Benghazi.

GOP lawmakers have claimed that the Democratic presidential nominee broke the law by lying under oath about her private email setup during her marathon appearance in October.

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Next month, Republicans on the House Judiciary Committee plan to make the issue a central part of a hearing with senior officials from the FBI, a committee aide said on Thursday.

Legally, the GOP faces a tough case. Politically, however, raising the perjury allegations would be a way to keep the issue of Clinton’s truthfulness in the public eye throughout the fall as she battles Republican nominee Donald Trump Donald John TrumpBiden leads Trump by 36 points nationally among Latinos: poll Trump dismisses climate change role in fires, says Newsom needs to manage forest better Jimmy Kimmel hits Trump for rallies while hosting Emmy Awards MORE for the White House.

Proving that someone committed perjury means overcoming a high hurdle: that the person knowingly told a falsehood under oath.

Convincing lawyers at the Department of Justice to take the case would also be difficult, because prosecutors would have to prove that what the former secretary of State said during the 11-hour hearing was directly at odds with the truth.

“There is no case,” said Stephen Ryan, a former federal prosecutor and general counsel for the Democratic-run Senate Government Affairs Committee, bluntly.

“Even if you tried to step back from the politically laden nature that this was the Democratic presidential nominee and you look at it, there’s no way the Department of Justice would touch a case like that.”

“There’s just no appeal to this case, other than the political appeal,” added Ryan, who said he is not involved in the presidential race.

Politically, hearings, letters and the other trappings of Washington could be useful for the GOP.

Polls have consistently shown that voters have doubts about Clinton’s honesty and trustworthiness.

New Hampshire Gov. Maggie Hassan, the Democratic candidate for the Senate in her state, even was tripped up this week. On three occasions, she sidestepped questions from CNN about whether she believed Clinton was honest before her campaign released a statement underlying her trust in the presidential nominee.

Even if the perjury allegations don’t save Trump, they could help down-ballot Republicans fighting against the current. Polls in Virginia and Colorado, both battleground states, have shown Trump running behind Clinton by double-digits.

The GOP heads of the House Judiciary and Oversight committees outlined the potential case against Clinton in a joint letter this week to Washington’s top federal prosecutor.

In their six-page letter, Reps. Bob Goodlatte Robert (Bob) William GoodlatteNo documents? Hoping for legalization? Be wary of Joe Biden Press: Trump's final presidential pardon: himself USCIS chief Cuccinelli blames Paul Ryan for immigration inaction MORE (Va.) and Jason Chaffetz Jason ChaffetzThe myth of the conservative bestseller Elijah Cummings, Democratic chairman and powerful Trump critic, dies at 68 House Oversight panel demands DeVos turn over personal email records MORE (Utah) pointed to four instances during which the former secretary of State “appear[ed] to implicate” two criminal laws barring perjury and false statements.

“The evidence collected by the [FBI] during its investigation of Secretary Clinton’s use of a personal email system during her time as secretary of State appears to directly contradict several aspects of her sworn testimony,” they told U.S. Attorney Channing Phillips.

The Justice Department decided last month not to press charges against Clinton for mishandling sensitive material after a yearlong FBI investigation.

Goodlatte and Chaffetz, in their letter, noted that the FBI discovered classification markings on three of the emails in Clinton’s inbox, seemingly disproving her assertion that “nothing was marked classified at the time I sent or received it.”

But in a letter to Capitol Hill this week, the FBI’s congressional liaison noted that those markings were incomplete, might have been made in error and were buried in a chain of emails.

The fact that Clinton received messages with those partial markings, Jason Herring wrote, “is not clear evidence of knowledge or intent.”

In another case, the GOP chairmen point to Clinton’s claim before Congress that her attorneys “went through every single email” while deciding which emails belonged in a federal storehouse and which could be deleted.

Comey later said that, in fact, her attorneys “did not individually read the content of all of her emails” but instead looked at “header information” and “search terms” to separate the roughly 30,000 emails that Clinton claimed were work-related from the similarly sized batch of messages that she said were personal. Comey said that the FBI discovered “several thousand” allegedly personal emails that were actually related to her official duties.

Those two statements are not necessarily at odds.

“’Went through’ and ‘read’ are two different things,” said Stephen Gillers, a law professor at New York University.

“There’s some ambiguity there,” he added. “Consequently, there’s some uncertainty about whether the fact she was asserting — ‘went through’ — is false, since it doesn’t necessarily mean ‘read every email.’”

Partly because of those types of ambiguities, it’s not common for perjury charges to be brought over testimony before Congress.

“The questions of the witnesses in Congress tends to be sloppier and looser,” said Charles Tiefer, a law professor at the University of Baltimore and former lawyer for both the House and Senate, who recently wrote a book called “The Polarized Congress.”

“Congressmen leave far more wiggle-room than professionals like prosecutors questioning witnesses on the witness stand.”

Rep. Trey Gowdy Harold (Trey) Watson GowdySunday shows preview: Election integrity dominates as Nov. 3 nears Tim Scott invokes Breonna Taylor, George Floyd in Trump convention speech Sunday shows preview: Republicans gear up for national convention, USPS debate continues in Washington MORE (R-S.C.), the chairman of the now largely defunct Benghazi committee, is a former prosecutor who is known for approaching congressional witnesses with precise, strategic lines of questioning. But other Republican members of the committee don’t have the same background.

Spokespeople for Chaffetz and Goodlatte did not respond to inquiries about the merits of the legal arguments.

Democrats have written off the GOP’s call for a prosecution, insisting that the move is merely a political gesture meant to attack Clinton’s credibility.

“It is clear that Secretary Clinton was telling the truth based on the facts she had at the time, and this Republican perjury referral is making a mockery out of congressional authority and trivializing our procedures for political purposes,” Rep. Elijah Cummings (D-Md.), the ranking member of the Oversight panel, said in a statement.

To be sure, Clinton has repeatedly made statements about her email system over the course of the last year and a half that were later proven false by the FBI.

She has been forced to walk back her claims that there was no classified information on the messages she sent and received. A total of 113 emails contained information that was classified at the time the messages were sent, Comey asserted last month.

She also insisted that all of the work-related emails were given to the State Department for safekeeping, though in fact thousands were marked as personal and deleted.

The FBI has every right to launch a preliminary investigation into allegations that she lied to Congress based on the recommendation of the GOP chairmen, noted Gillers, the professor from New York University.

But unless they can dig up concrete proof that Clinton knew she was lying under oath, the probe might end there.

“If the case were just, ‘Did Hillary Clinton tell things to Congress that turned out not to be true?’ I think the answer there is, yes,” said Tyler Doyle, a partner at the Houston-based law firm Smyser Kaplan & Veselka.

“Can it be said with certainty, beyond a reasonable doubt, that she willfully made such a statement?” he added.

“That’s tougher.”