BURLINGTON, Vt.—Jane O’Meara Sanders has helped Bernie Sanders through more than a dozen elections over the years, winning most of them. Now, as the Democratic presidential nomination looks increasingly out of reach for a second time, she is his chief sounding board for determining his next steps.

The candidate’s wife of 32 years and most trusted political adviser for even longer, Mrs. Sanders says that if the campaign ends, the pair will help to elect former Vice President Joe Biden and continue to press for their shared...