The short answer is, Medicare won’t but Medicaid will.
Medicare Part A only pays a limited amount for nursing facility care for a short period, and only under special circumstances.
Medicare covers only medical care in a skilled nursing facility following a minimum three-day hospital stay, and only for as long as the patient needs daily skilled medical care or therapy. It does not cover what’s called “custodial care,” meaning long-term residence in a nursing home.
If your father qualifies for Medicaid, on the other hand, it can cover the full cost of his nursing home bills. (Be aware, though, that many nursing facilities have only a limited number of beds for Medicaid-pay residents.) Medicaid can keep paying for as long as he lives in a nursing facility. To qualify for Medicaid, he must have a very low income and few assets. You can find specific information about Medicaid eligibility and nursing home coverage for your father's state online at the Medicaid/Medicare section of the federal government's "govbenefits" web site.