If the past is any guide, little of the money donated will do any of this. During the 2014 midterms, the Conservative Action Fund reported receipts of $241,355, according to FEC records. Almost half went to a single digital campaign firm, presumably used to create and send the fundraising pitches. Another $25,000 was paid to the legal and compliance firm run by the group’s treasurer, Dan Backer, who has also been associated with dozens of similar groups, including Stop Hillary PAC and the Committee to Draft Judge Andrew Napolitano.

All this raises the question: Is the Conservative Action Fund a scam?

“If anybody’s getting scammed, it’s me,” quipped Shaun McCutcheon, the group’s chairman, who told me he has made sizable contributions (more than $275,000 since 2011, according to FEC records) to get the PAC off the ground. I asked Mr. Backer whether those petitions—to draft Allen West, say—are ever sent. Sometimes, he replied, but sometimes not. It depends whether the number of signatures reaches critical mass. And what about fundraising off of the names of famous, but hypothetical, candidates? “They’re not private brands like Coca-Cola,” Mr. Backer replied. “They are public figures.”