Offering Donors Secrecy, and Going on Attack

The American Future Fund, organized under a tax code provision that lets donors remain anonymous, is one of dozens of groups awash in money from hidden sources and spending it at an unprecedented rate, largely on behalf of Republicans. The breadth and impact of these privately financed groups have made them, and the mystery of their backers, a campaign issue in their own right.

“I think most people are very comfortable giving anonymously,” Mr. Sembler said. “They want to be able to be helpful but not be seen by the public as taking sides.”