Democratic presidential candidate Sen. Kamala Harris made her party’s left-wing base happy this week. But in doing so, she might have made Democrats less attractive to general-election voters.

In a CNN town hall Monday, Ms. Harris endorsed “Medicare for All.” Pressed about whether the proposal would abolish private health insurance, the California senator breezily declared, “Let’s eliminate all of that. Let’s move on.” After Republicans jumped on her for this policy’s radicalism, a Harris adviser said the attacks were “good...