Medicare generally pays for short-term care for rehabilitation purposes, which is referred to as skilled-nursing care.  Medicare covers 100 days in a skilled-nursing facility but only after three consecutives days in a hospital (which does not include the discharge day).  Medicare covers 100% of the cost for the first 20 days.  The next 80 days, your parent is responsible to pay $148.00 per day, which likely will be picked up by the secondary ("gap") insurance, and Medicare covers the balance. 

Medicare will only pay for services provided by Medicare-certified facilities.

Two other facts we learned were:

1. If your parent's doctor is recommending skilled-nursing care, your parent will have 30 days to make that decision.  In other words, your parent can go directly home after a hospital stay and take a month before deciding whether to enter a skilled-nursing facility.
2. If your parent uses up the entire 100 days of coverage in a skilled-nursing facility as our dad did, then the only way to replenish it is for your parent to be out of the hospital and/or skilled-nursing care for 60 consecutive days.  Then the next time your parent is in the hospital for at least three consecutive days, coverage for 100 care days is replenished.  With our dad, we found ourselves nervously counting the days between his skilled-nursing care stays.  This was unbelievably stressful.  In fact, one time our dad was at the 58-day mark when he had to go back into the hospital, and coverage for the next 100 days was lost.