If Hillary Clinton turns in another disappointing performance in the June 7 California primary, Peggy Noonan can see her doing something desperate—like picking Bernie Sanders as her running mate. “It would help keep Sanders voters, who often threaten to go elsewhere if Mrs. Clinton is the nominee, in the tent. It would also unsettle Trumpworld. They see Bernie supporters as potential Trump supporters in the general election.”

But not everyone will stay in the tent. In the next election cycle Ms. Noonan predicts some Democrats...