A women 62 is collecting social security off her husband's record .
She doesn't have enough credits of her own. When she turns 65
Will she have to pay the full premium for Medicare ?

This llink may lead to the answer even though it initially talks about free Medicare for spouses in the circumstances you described. There is a second link in the article for those who do not qualify for free Medicare. Follow through it a bit and it MAY help or may not.
Haven't seen much of you lately pastor. You always have interesting questions.
Medicare Interactive - Under what conditions would my spouse's work history qualify me for premium-free Part A? (http://www.medicareinteractive.org/page2.php?topic=counselor&page=script&slide_id=338)

Thank you

What about Medicaid? If she has that (state run), it should continue to pay her Medicare premium, as well as cover the Medicare deductible and additional coverage.

She doesn't qualify for Medicaid in Florida