WASHINGTON—Hillary Clinton’s lead in presidential-election polls has Wall Street increasingly focused on the battle for control of Congress—and bracing for a less friendly environment if Democrats retake the Senate and give new clout to the party’s left wing.

“It’s not Hillary Clinton we are worried about. It’s the influence that the liberals have on her,” said Richard Hunt, president and chief executive of the Consumer Bankers Association trade group. He cited Democrats on the Senate Banking Committee, particularly Elizabeth...