The League's decision to drop its sponsorship gave rise to the CPD, which was initially chaired by the former heads of the Democratic and Republican parties. Today, the co-chairmen are Frank Fahrenkopf, Jr., the former chairman of the Republican National Committee and the president and CEO of the American Gaming Association, and Democratic strategist Michael McCurry, who was White House press secretary under President Bill Clinton.

Despite its leadership, backers of the CPD say, the organization has shown that it is not in thrall to the major parties. Minow, who authored a New York Times op-ed defending the CPD, points to the group's 2004 rejection of a "memorandum of understanding" concerning the debate details and its refusal in 2008 to delay the debates at the request of Sen. John McCain, who cited the financial crisis as the reason for his request. (The CPD hasn't always stood its ground: In 1988, it agreed to demands from the campaigns that two debates be held instead of three, and in 1992 it had to scramble to meet the conditions set forth by the major parties, who worked out a deal with no one from the CPD present.)

"I'm very proud of the commission," he told CBS News. In his op-ed, Minow described the debates as "the one time when the major candidates appear together side by side under conditions they do not control." A representative for the CPD did not respond to multiple requests for an interview with CPD executive director Janet Brown.

Schroeder, the debate expert from Northwestern University, said that it's "inevitable" that the commission would have a relationship with the major parties. "But is it collusion? I don't think so," he said. Schroeder says the CPD allows private agreement between the two parties, though he said the negotiations this year were informal and the agreements do not cover what questions will be asked.

Farah wants to see the CPD replaced by a citizens' debate commission made up of civic leaders that would be "genuinely nonpartisan" and not be funded by corporations. Under the CPD, the debates are sponsored by Anheuser-Busch Companies and other corporations and foundations. He also dismisses concerns that if third party candidates are allowed to participate, the major party candidates may choose drop out - as Carter did in 1980 - potentially depriving the American people of one of their few chances to see the major candidates in a relatively unfiltered setting.

"At this point in history, a candidate cannot avoid an actual presidential debates without appearing to be totally cowardly," he said. "So the public has leverage."

Buchanan said that the requirements of the CPD mean that "it's enormously difficult for a third party candidate to make it unless he has an enormous amount of money or is an extraordinarily popular figure."

"They say if you don't have 15 percent you don't get in the debates, but if you don't get in the debates you don't get 15 percent," he said.