DAVENPORT, Iowa—Sen. Elizabeth Warren’s call for a Medicare-for-All health plan drew heightened scrutiny from her Democratic presidential rivals after she released a highly anticipated plan to pay for it.

Two leading Democratic candidates—former Vice PresidentJoe Biden and South Bend, Ind., Mayor Pete Buttigieg—had criticized Ms. Warren’s plan to expand government-run insurance to all Americans. They also found fault with her proposal to pay for it with $20.5 trillion in new funding, largely generated from employers and the...