African-American voters back Medicare for All more than other groups, polls show, but the policy’s two chief proponents in the 2020 Democratic presidential race haven’t been able to translate that into widespread black support.

Instead, Sens. Bernie Sanders and Elizabeth Warren continue to lag well behind Joe Biden with black voters. The former vice president has been a chief critic among Democrats of Medicare for All and prefers a more moderate expansion of health insurance. In a recent South Carolina poll, he led Mr. Sanders...