Two major developments shook up the Democratic nominating contest during the past week: Former President Barack Obama spoke out, and Mayor Pete Buttigieg surged to the top of the polls in Iowa. Both reflect clear-eyed appraisals of public sentiment.

In remarks to a group of liberal donors, Mr. Obama politely but firmly urged Democratic candidates not to veer too far left in their quest for primary voters. “This is still a country that is less revolutionary than it is interested in improvement,” the former president said. “They...