A spokesman for the Ricketts family declined to comment.
Marlene Ricketts is married to Joe Ricketts, the billionaire founder of T.D. Ameritrade. One of their four children, Pete, is the governor of Nebraska. Another son, Todd, is co-owner of the Chicago Cubs and was a top fundraiser for the short-lived presidential campaign of Wisconsin Gov. Scott Walker.
In January, Marlene Ricketts help jump start the newly-formed Our Principles PAC, giving the group $3 million in three separate contributions.
The super PAC also received $7,500 from Illinois businessman Richard Uihlein. In just one month, Our Principles has emerged as the biggest anti-Trump spender of the cycle, plowing more than $3.8 million into ads that showcase contradictory positions he has taken over the years.
Katie Packer, the Republican strategist leading Our Principles PAC, said Trump's tweet was an effort to silence his critics.
"It's what we've come to expect from Donald Trump," she said. "He doesn't have any answers for anything we've put up on TrumpQuestions.com, so he tries to bully and intimidate and threaten people. It’s designed to scare people out of contributing, but I don’t think any of our donors were deluded into thinking they wouldn’t become targets of Trump. They knew this was coming."
Trump spokeswoman Hope Hicks fired back in a statement, saying: "That is rich. Someone spending millions of dollars of other people's money to disparage Mr. Trump characterizes his defense as bullying?"
"Mr. Trump will continue to tell it like it is, especially, where out of touch establishment elites are concerned," she added.
For her part, Packer said Our Principles is not backing down, saying there is a spate of new interest from prospective donors in the wake of Trump's victory in the South Carolina primary.
"I think people understand the threat is very serious," she said, adding, "We expect we’ll be able to have a serious campaign in the March 1 states."
Anu Narayanswamy contributed to this report.