Mississippi Republican state Sen. Chris McDaniel is still not giving up after his primary loss in the race for U.S. Senate. McDaniel, who lost his Republican Senate primary challenge to incumbent Sen. Thad Cochran in late June, formally filed a challenge Monday with the Mississippi Republican Party’s executive committee over the election results of the runoff election. "They asked us to put up or shut up," McDaniel said in a short press conference Monday. "Here we are. Here we are with the evidence." Cochran holds a strong lead in post-election polls over Democratic nominee Travis Childers. But Democrats are hoping the bitter split between Cochran and McDaniel supporters might make the race competitive. The longer cries of a stolen election linger in the race, the better their chances. McDaniel began vocally challenging the election results shortly after the runoff election was held on June 24, claiming that voter fraud kept him from clinching the nomination. While Cochran won the runoff election by 7,667 votes, McDaniel's lawyer argued that the state party should nullify the results due to improperly cast votes. "We anticipate that after they review the challenge that they'll see that Chris McDaniel clearly won the Republican vote in the runoff," attorney Mitch Tyner said Monday. "We are not asking for a new election, we are simply asking that the Republican Party actually recognize the person who won the runoff election." Despite the state Republican Party verifying Cochran's win on July 7, McDaniel began accusing the Cochran campaign of wooing Democrats, and particularly African-American voters, to support him in the runoff contest. The campaign claims to have found 3,500 instances of voters who cast a ballot in both the Democratic primary and the Republican runoff election and upward of 10,000 votes that should be challenged, according to NBC News. In addition to claims of improper ballots, the McDaniel campaign's complaint cited allegations of Cochran's campaign paying operatives to buy Democratic votes. The allegation gained prominence last month when a conservative pro-McDaniel blogger Charles C. Johnson interviewed a pastor, Steve Fielder, who said he was recruited to hand out cash for votes on Cochran's behalf. Mississippi Attorney General Jim Hood said last week, however, that Fielder had not only recanted his story but now claimed Johnson paid him $2,000 to spread phony vote-buying allegations. Mississippi's Republican primary has been marred by scandal since before voters headed to the polls. A pro-McDaniel blogger and three others were arrested back in May over allegations of a plot to photograph Cochran's ailing wife in a nursing home. And the race took a dark turn in late June when one of the people who was arrested, tea party activist and lawyer Mark Mayfield, was found dead of an apparent suicide.