BRADENTON BEACH, Fla. — The billboard flickered from the side of a truck, displaying an image of Representative Vern Buchanan, Republican of Florida, wearing a yachtsman’s cap. Keith Fitzgerald, a local dignitary invited by the group Floridians for a Fair Shake, stood before it as he tore into the lawmaker’s record.

The congressman embodied “deep and profound corruption,” Mr. Fitzgerald told a thin crowd. The nautical caricature of Mr. Buchanan, a wealthy auto dealer, alluded to his purchase of a multimillion-dollar yacht on the same day he voted for a bill cutting upper-income tax rates.

Floridians for a Fair Shake has criticized Mr. Buchanan for months, with paid advertising, campaign workers, and events like this, on a recent Sunday in a beachside parking lot. Yet Mr. Fitzgerald, a former Democratic state legislator and something of the guest of honor, confessed, “Honestly, I don’t know a whole lot about this group.”

“They told me what they were doing,” he continued. “I’m not sure where the money comes from.”

A structure unknown even to some of those involved, Floridians for a Fair Shake and 13 other groups around the country are funded and coordinated out of a single office in Washington, with the goal of battering Republicans for their health care and economic policies during the midterm elections.