Establishment Republicans are probably right to believe that a government shutdown would hurt the GOP. But Republican office-holders are probably right to believe that supporting a shutdown would help them with GOP primary voters:
Overall, 71 percent of those surveyed opposed a shutdown, while 23 percent favored a shutdown. Among Republicans, 53 percent opposed, versus 37 percent who favored.[…]
Among Republicans who called themselves conservative, those who said they are very conservative favored shutdown by 63 percent to 27 percent, while those who said they are somewhat conservative opposed shutdown by 62 percent to 31 percent. Overall, Republicans who call themselves conservative were evenly split on the issue, 46 percent to 46 percent.
Two things: (a) if a very conservative voting group shows up on election day — and that’s likely in a lot of Republican primaries, especially in places like TN, SC, and KY — they’ll favor a candidate who shut the government down and (b) the non-incumbent Republican candidates will likely be pro-shutdown teahadists, so a shutdown certainly won’t hurt many Republican incumbents on primary day.