Of course, in the Rethuglican / New Confederate / Stupid Party, "establishment" just means he's not a certifiable lunatic, just a common sociopath. To wit: Thom Tom said people receiving public assistance for medical disabilities should "look down on" poor people receiving public assistance due to other factors << cough their race cough>> The desired effect would be to create what Thom Tom called a "divide and conquer" situation, no doubt providing a rationale for assistance programs getting slashed and taxes on Thom Tom's wealthy contributors being cut. That remark -- among many yet to be made -- should stick to Thom Tom like tar.
BONUS: Charles P. Pierce describes the "Establishment Republican" brand Tillis represents:
... Tillis is as blackhearted a reactionary as one currently expects a champion of modern conservatism to be. He will be central to the attempt to recreate the newly insane state legislature of the newly insane state of North Carolina on a national basis. This should puzzle no one. The long game of corporatized, radically extreme Republican politics is coming down to the final moves. Nothing -- and certainly not the nomination of "Establishment" hero Thom Tillis -- can stop that now.