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Chris McDaniel lost the GOP Mississippi Senate primary to six-term incumbent Sen. Thad Cochran by some 6,700 votes, if the official tally is to be believed.

But McDaniel refuses to concede. He and his supporters continue to mull legal challenges, based on the still unproven claim that Cochran's win was powered by voters who shouldn't have been allowed to cast runoff ballots last week.

McDaniel called the election "shameful" in an email today, and said the only reason Cochran "stole" the election was "thanks to illegal voting from liberal Democrats."

"Last week's runoff election was a sham, plain and simple," McDaniel wrote, adding he has a "long fight ahead" and asking for money to help "mount the legal challenge that this case deserves."

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The Cochran campaign openly courted Democrats, specifically African-American voter, after McDaniel won the June 3 primary, which helped seal Cochran's victory three weeks later. This is completely legal in the Magnolia State as it is an open primary, but it is illegal if a voter cast a ballot in the Democratic primary and then also voted in the GOP runoff on June 24. This is exactly what McDaniel's campaign says happened.

McDaniel communications director Noel Fritsch says they have found about 4,900 ballots that have voting irregularities, which he says the "vast majority consist of ineligible crossover voters," or voters who illegally participated in both the primary and the runoff. They have examined the books from 53 counties, but 29 counties remain, according to Fritsch.

Fritsch says they also have not looked at any of the 19,000 absentee ballots either, but they have 150 staff and volunteers spread across the state comparing poll books to make sure voters ineligible didn't cast ballots twice.

He does not believe they need to find more than 6,700 votes in order to throw out the election, saying they just need to find enough voter irregularities, but election experts in the state say that's unlikely.

While some states have mandatory recounts when the margins are narrow, that does not exist in Mississippi.

"There is a very specific procedure when ballots are challenged and the grounds for it are very limited," Matthew Steffey, a professor of election law at Mississippi College School of Law in Jackson, told ABC News.

He noted the challenge must be done in person as the ballots were being cast last Tuesday.

"The reason the day-of challenge is so important is…it's not enough to say 'Hey we went through the books and found voter irregularities,' you've got to show who these people voted for," Steffey said. "You can't just speculate that all the irregular votes went to your opponent so 'then we are going to re-do the election,'…that's the thing with voting, it's anonymous and private and you can't make a court case by speculating who they voted for.

"These irregularities pale in comparison to Florida in 2000 and then the Supreme Court of the United States said stop the recount, stop the challenges, certify the election," Steffey noted. "I don't think they've show anything."

There seems to be no precedent for the kind of legal challenge McDaniel and his supporters are attempting to mount. The McDaniel campaign has not formally begun any legal action, but conservative voter watch dog group True the Vote filed suit against the Mississippi Republican Party and the Mississippi Secretary of State Tuesday. They are calling for the state to preserve and give them access to election records, before the election is certified. The McDaniel campaign supports the effort.

"This issue strikes at the heart of election integrity," True the Vote president Catherine Engelbrecht said in a statement. "Confidence in our voting process risks damage beyond repair when politicians of either party are willing to flout election laws in the name of self-preservation. Voters deserve to know that election processes and protocols were followed - especially in a close outcome."

Joe Nosef, the chairman of the Mississippi GOP, says all counties are going through the process of certifying their votes over the past few days and it will become official Monday. He says there has been a "general misunderstanding that there needs to be a rush to view the books before they are certified. It's the opposite of the truth because it begins the opportunity for review."

"I think for the good of all of us it's time stop all the accusations," Nosef said. "If people feel like there was something done wrong then bring it forward. They are hurting the process and hurting the party with these accusations and theories of wrongdoing. If there has been something done wrong, let's see it."

Cochran's top strategist, Stuart Stevens, calls McDaniel's actions "an absurd public meltdown not based in reality," noting he thinks this is all about retiring McDaniel's debt from the primary.

"Chris McDaniel is accusing the governor and all elected officials in the state of Mississippi of engaging in a monstrous fraud and the inability to conduct a free and fair election. His proof? He lost," Stevens told ABC. "He's embarrassing the state, he's embarrassing the GOP, he's accusing the state of Mississippi of being a banana republic because more people participated in a Republican election … most people would that think that's good news. He thinks it's a fraud because he lost.

"In six months, Chris McDaniel will be an asterisk and Thad Cochran will be a U.S senator," Stevens said, "and he could have had some sort of career."

This story has been updated since it was first posted.