WASHINGTON—At a breakfast fund-raiser last year at the Liaison Capitol Hill hotel, former lobbyist Paul Equale pulled up a chair next to Sen. Richard Durbin. As they chatted, the Illinois Democrat told him about a recent breakthrough in his efforts to push through a bill to cap debit-card fees.

In Washington, such shop talk between political insiders is so routine that it hardly warrants mention. For Mr. Equale, however, it yields intelligence that fetches good money on Wall Street.

Mr....