Yes, that’s why the GOPe is taking the threat of the shutdown over Planned Parenthood seriously and also why the conservatives are willing to have the fight. Cruz is a leader and they are following his lead.
The electorate is of course a factor because the GOPe knows they are behind the conservatives in this fight. But with Trump out of the picture, that electorate wouldn’t be going to Bush, it would be going to a non-establishment candidate. The electorate would be making their voices heard one way or the other.
For every tiny nitpick of a Cruz vote you can make, we can point to Trump’s long history of supporting liberal policies and funding Democrat candidates. Somehow I doubt you’d give Cruz a pass if he had donated money to Pelosi.