No Labels made a big announcement Thursday morning — but it wasn’t that they are running a third-party presidential “unity ticket” in 2024. That highly anticipated decision, the group’s leaders say, won’t be made until early March, after Super Tuesday.

The nonprofit political group instead announced it has asked the United State Department of Justice to investigate potential criminal charges against Democratic-leaning operatives and political groups working to thwart No Labels from getting ballot access. The move indicates No Labels is taking a more aggressive posture toward those seeking to prevent the group from running a third party “unity ticket” with a moderate Republican and Democrat.

In a January 11 letter to the Justice Department, signed by former Democratic vice-presidential candidate Joe Lieberman and several other No Labels leaders, the group alleges there is a “highly coordinated, conspiratorial, partisan, and often unlawful conspiracy — involving individuals both inside and outside government — to deny Americans their constitutional right to choose leaders to represent them.” They cite several federal statutes related to voter suppression and civil rights, as well as the RICO statute.

“This is a big day for No Labels,” a prominent Chicago attorney and No Labels volunteer, Dan Webb, who signed the letter, said Thursday. “We’ve been taking it a long time and we decided it was time to fight back.”

The letter details multiple incidents of alleged harassment and intimidation against No Labels members, donors, and potential candidates, which the group says goes beyond First Amendment protected speech or usual political dirty tricks. In one instance, a Lincoln Project representative and former Democratic Party finance director threatened No Labels co-founder Holly Page at a private lunch, telling her, “You will never be able to work in Democratic politics again.” Ms. Page lost her job with the U.S. ambassador to Malta within weeks.

In another instance, a mobile billboard with the faces of No Labels chief executive, Nancy Jacobson, her husband, and Donald Trump was paraded around Georgetown during the weekend of the White House Correspondents’ Association dinner, with the message, “Nancy and Mark need to stop playing around with America’s future to make rich donors happy.”

“Who do they think they are? Tony Soprano.” No Labels national co-chairman and former governor of North Carolina, Pat McCrory said Thursday.

“I want to emphasize this: the right to obtain a ballot line is just as protected by the US constitution as the right to register to vote,” No Labels chief strategist, Ryan Clancy, said. “But powerful forces in Washington clearly don’t respect this right.”

The letter lists several meetings involving the Lincoln Project, Third Way, and other Democratic and anti-Trump Republican politicos — one including former Biden chief of staff Ron Klain — in which attendees discussed how to pressure potential candidates and donors from affiliating with No Labels. Anti-Trump groups say a moderate third-party ticket would hurt President Biden’s chances at re-election and help usher in another Trump presidency.

No Labels leaders said the Justice Department has not responded to their letter. A No Labels national co-chairman and former chief executive of the NAACP, Benjamin Chavis, called this “a brazen voter suppression effort.”

No Labels has obtained ballot access in 14 states and is working to secure it in another 13. The group’s chief strategist, Ryan Clancy, tells the Sun that No Labels expects to have secured ballot access in 32 states by later this year, and will secure the remaining states after it names a ticket.

“Ross Perot at this point in 1992 hadn’t even started gathering signatures yet, and he ended up on all 50 states,” Mr. Clancy says. “We are ahead of the game.”

Mr. Clancy says No Labels will only run a “unity ticket” if “there’s an opening.” As it seems increasingly likely that President Trump will win the New Hampshire primary next week and the Republican presidential nomination for a third time — making the 2024 election another Biden-Trump matchup — the prospects of a No Labels ticket are getting brighter.

“If it’s Trump and Biden, we think there’s an opening at least in the numbers,” Mr. Clancy says.

No Labels’ polling suggests a ticket with a Republican at the top and a Democrat in the vice-presidential slot would do best against Messrs. Trump and Biden. The ticket would need to get 34 percent of the vote to win, according to their models. Several names have been floated in recent months, including Chris Christie and Nikki Haley. A former Republican Maryland governor, Larry Hogan, left No Labels’ board last month and endorsed Ms. Haley.

Several No Labels leaders have expressed their desire to prevent another Trump presidency, yet it is Democrats who are trying hardest to thwart No Labels from running a presidential ticket. Mr. Lieberman called this “hypocrisy” Thursday.

“There is a lot of talk lately about democracy being on the ballot in 2024, and in many ways it is,” Mr. Lieberman said. “The conspiracy we have alleged to the Department of Justice today is no less than an attempt to knock the legs out from under American democracy …. And I must say it’s particularly ironic and hypocritical when it comes from people who claim to be concerned about existential threats to democracy.”