Medicaid is for the poor, many of whom work full time. It also covers the disabled, and sixty percent of nursing home residents. To qualify for long-term care you must burn through almost all your assets.

Medicare is for people 65 and older. Don't kid yourself that the 1.45% Medicare tax (matched by the employer) covers the cost of the program. It only covers Part A, hospitalization. Part B covers doctor visits, lab tests, surgeries and medical devices is paid for by premiums. Most seniors pay $109/month depending on income. But this only pays 25% of the cost, 73% is paid from general revenue. 

Both programs are important components of our social safety net.