Heritage says it would be happy to debate but would send the foundation's senior labor policy analyst, James Sherk, instead.
The AFL-CIO has said the invite was only good for DeMint. Neither side appears willing to budge, so a debate looks unlikely.
Heritage spokesman Michael Gonzalez told the Washington Examiner: "We think the debate should be with Sherk," a prolific writer and researcher. "What we want is a policy-rich debate."
Asked repeatedly if DeMint himself was therefore not available to debate, Gonzalez declined to directly respond.
AFL-CIO spokesman Josh Goldstein said that was no good: "Jim DeMint is the face of the Heritage Foundation and conservative ideology to lower the minimum wage; if he thinks his position is what’s best for the country, he shouldn't be afraid to make the case publicly."
Trumka's labor federation has been a major advocate of the current push to increase the minimum wage, which would make low-paying non-union labor less economically competitive. The conservative Heritage Foundation opposes an increase, arguing it will do more harm than good.
The challenge was first issued in a "hand-delivered" letter March 11, according to Goldstein. They are apparently flexible on the location. "[W]e aren't saying it has to be held at any particular location," Goldstein said.
Gonzalez said they responded shortly after the letter was received, offering Sherk. "I don’t understand why they’re implying they haven’t heard from us."
Be certain to read the Examiner's own Phil Klein on why hiking the wage would be bad for the economy.