But some of the most influential Republicans in the House have been singed by the firestorm.
Not all influential Republicans, however, support the flat tax concept.
In interviews this week, several influential Republicans attacked the strategy of creating minority districts as short-sighted.
The attack on the Rockefeller commission proposal echoes criticism from two other influential Republicans.
She is one of seemingly few influential Republicans who are pro-choice.
Nevertheless, it was dismissed as unworkable by some influential Republicans.
"He's the only cabinet member who hasn't really stepped into the national dialogue in a persuasive way," one influential Republican said.
Most influential Republicans concede that they do not expect the party to benefit from the inquiry.
But economic issues may start looming large, too, particularly for influential upstate Republicans.
Some influential Republicans in Congress began to voice complaints as well.