(Timothy D. Easley/AP Photo)

Mississippi State Sen. Chris McDaniel officially announced the beginning of a legal effort to challenge the results of his primary fight against six-term incumbent Sen. Thad Cochran.

The campaign formally filed a challenge with the Mississippi Republican Party's executive committee, the official first step to mounting a legal challenge.

On June 24, Cochran beat McDaniel by over 7,600 votes and those results were certified unanimously by the party's executive committee. McDaniel never conceded, instead he almost immediately began accusing his opponent of "stealing" the election because Cochran was able to woo Democrats, specifically African American voters in the Magnolia State, to support him in the run-off. This is legal, but not if the Democrats also voted in their primary three weeks earlier.

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Since that time McDaniel volunteers have been combing through voter rolls and in a press conference today McDaniel's attorney Mitch Tyner said they have found 3,500 cross over voters, 9,500 votes they believe have irregularities, and 2,275 absentee ballots they also believe were "improperly cast." Tyner said they believe they have 15,000 votes "cast that should not have been."

"We are not asking for a new election, we are simply asking that the Republican Party actually recognize the person who won the run-off election," Tyner said.

Tyner, who called today "a day we have all been waiting for," said their evidence shows McDaniel "clearly won" the run-off by 25,000 votes. Tyner said he is getting that number by post-election polling they conducted that showed 71 percent of the Democrats who voted in the run-off did not plan to support the Republican in the general election. A Mississippi state law says a voter in the run-off must have the intent to cast the ballot for the same person in the general election.

Mississippi election law expert Matthew Steffey said this statute is "unenforceable because you can't quiz individual voters on what their intentions are in the voting booth because it violates their right to vote anonymously in a polling place," noting the concept would be "inconceivable in a court of law," and "unprecedented in American politics."

Steffey, a professor of election law at Mississippi College School of Law in Jackson, says the McDaniel team is "playing a very weak hand."

"Lawyers have to make the case they can make, not the case they would like to make," Steffey said in an interview with ABC News. "And the very fact that we are talking about polls which Sen. McDaniel must know, certainly his lawyers know will have no role in court room litigation, can't possibly be the basis for judicial opinion….that' s not evidence, that's at least double hearsay, it may be worse than that."

Steffey notes the "most important number" is the cross-over votes and that has been their argument since the run-off.

"If he had a large number (of cross-over votes) we wouldn't be talking about polls and throwing out 71 percent of Democratic votes, he's doing that because it's all he's got," he said.

In the press conference, McDaniel told supporters and reporters gathered it's important to be "dispassionate about the facts."

"The facts they're on our side, the law is on our side," he said. "This is an opportunity for our party to take the lead on honest, good, and transparent government. As Republicans, we talk about the need for transparency, as Republicans we want open debate and dialogue, honesty, transparency, and integrity are hallmarks of the conservative movement. We anticipate the Republican executive committee will grant us a hearing, we anticipate they will do it in a public forum."

McDaniel who called the supporters gathered his "brothers and sisters" continued, saying the GOP is a "party that doesn't need decisiveness to win" and is "a party that does not need to play the race card to win."

"The integrity of the elections process in the state of Mississippi matters," McDaniel said. "But, likewise the integrity of the Republican Party and its primary system…it matters as well."

When McDaniel's attorney was asked if he thought anyone should to jail over the situation, Tyner said he wouldn't "predict…but if I had a choice, yes."

McDaniel has come under conservative criticism for continuing the fight. Most notably, conservative pundit Ann Coulter called on McDaniel last month to end his effort.

The Mississippi Republican Party couldn't be immediately reached for comment.