McDaniel's comments, which he made in an interview on Mark Levin's radio show Wednesday night, follow a runoff election on Tuesday in which Cochran defeated McDaniel. McDaniel and his supporters have objected to the vote outcome because of Cochran's efforts to get African Americans and Democrats to support the incumbent senator in the the Republican runoff.
It's not clear exactly where McDaniel got the 35,000 figure.
"Naturally sometimes it’s difficult to contest an election, obviously, but we do know that 35,000 Democrats crossed over," McDaniel said. "And we know many of those Democrats did vote in the Democratic primary just three weeks ago which makes it illegal."
Voters in Mississippi don't register by party and the state has open primaries. Voters are only barred from voting in one party's primary and then voting in another party's runoff, but voters who didn't vote in the initial primary are not barred from voting in a runoff election.
McDaniel also referenced a law that said a voter can only vote in one party primary if the voter plans to support the nominee of that primary in the general election. But that law was ruled unenforceable by a federal appeals court in 2008.
"We likewise know that we have a statute, a law in our state that says you cannot participate in a primary unless you intend to support that candidate," McDaniel said. "And we know good and well that these 35,000 democrats have no intention to do that. They’ll be voting for [Democratic nominee] Travis Childers in November. We know that. They know that. And so that makes their actions illegal."
"So we’re going to be fighting this," McDaniel continued.