WASHINGTON—As Sen. Elizabeth Warren develops her proposal for financing Medicare for All and reshaping how Americans pay for health care, she faces a complex set of challenges.

The Democratic presidential hopeful from Massachusetts could propose a plan to partly pay for a single-payer system by finding ways to reduce health-care costs, expanding budget deficits or adding new levies on the richest Americans. But replacing insurance premiums would likely require taxes on individuals and businesses.

And...