Mack has a lead of about 30 points in the primary to take on Nelson, but his candidacy has far from allayed the concerns of many Florida Republicans who continue to gripe about the weakness of the field. In addition to former Sen. George LeMieux (R-Fla.) and Tea Party-backed Mike McCalister, who are both competing for the GOP nod, former Rep. Dave Weldon (R-Fla.) announced in May he too would enter the race.

Jeff Cohen, Mack's campaign manager, told the debate organizer that a primary debate would only benefit Nelson, and that it would make sense for Mack and Nelson to debate instead.

Florida's Senate primary is set for Aug. 14.