Those groups' recent record is mixed. Democrats are hoping for a repeat of 2010 and 2012 races where the far right groups backed less-viable candidates who lost general elections in Colorado, Nevada, Delaware and Indiana. But the same groups also helped elect Lee, Cruz and Marco Rubio in the presidential swing state of Florida.

At FreedomWorks, PAC treasurer and policy chief Dean Clancy dismissed any notion that his efforts would hurt the party.

"Republicans make a mistake when they try to waffle on these issues or sound like Democrat-lite," he said.