As her rivals head to the exits, Elizabeth Warren is vowing to press on to a contested convention.

For Democrats, this was supposed be a moment to begin easing three years of built-up of anxieties. Instead, the launch of the 2020 presidential primary has left the party deeply unsettled and President Donald Trump gleeful about the chaos. Party leaders are on edge over embarrassing technical issues that marred this past week’s Iowa caucuses, as well as lower than expected turnout in the leadoff state. Front-runners Bernie Sanders...