Maybe. The primary voters literally don't care, many of them actually *want* euro-style $20/gal gasoline to encourage everyone to ride bikes and take the bus.

It could actually be a problem in the general election. So it's possible that the party will intervene in the primary to ensure Newsom isn't the nominee (maybe a Swalwell file or the like?). There are rumblings on the left that they need some mid-west moderate-ish white guy for 28. Even some on the far left, they're getting tired of losing and consequences... eight years of some combination of Vance/Rubio would be mean at least a couple more SCOTUS picks.