A billionaire investor whose family owns the Chicago Cubs is pressing ahead with a multimillion-dollar pro-Republican political campaign, bucking a political furor that emerged when the effort first become public.

Joe Ricketts, the founder of what became online brokerage TD Ameritrade Inc., plans to spend $10 million airing ads supporting GOP nominee Mitt Romney and another $2 million to help Republicans running for Congress. The ads will begin airing this week.

The...