Asked to voluntarily resign

I am a 53 year old divorced female in the Kingston, N.Y. area. Employed by local Catholic Hospital in a Supervisory capacity for past 20 months. Received an outstanding anual job evaluation, plus I was given a special presidential achievement award after being there only a few months. Just recently completed series of management training sessions which was mandatory for entire management staff. All of a suden yesterday, with no warning, I was asked by my immediate supervisor to meet with him and his boss. I was told in that meeting what a good person I was, and how well I was liked by everyone, and what a hard worker I have been etc., but "I was just not the right person for the job". I asked why I got such a good evaluation and had no indication prior to this that they felt this way. The answer was "well, when you are in management things are handled differently". If you were just a regular employee you would have received verbals, then written warnings etc.
I asked if what he was saying is that he wants me to resign.
The answer was yes, but they would prepare a severance package, and give me a few days to think it over. He said they were not saying I had to leave tomorrow, but that of course I couldn't stay on indefinitely. I have worked my entire life, and never been in this position before. Please give me some advise. This isn't right. I have done nothing wrong. He even said he asked Human Resources if there was another job elsewhere in the hospital where my "people skills" and talents and abilities could be used, because the hospital hated to loose good people like me, however, Human Resources had nothing available in my income level. Please help me.

You are mid-level management. In this day and age, unfortunately, your group is the first to go when there might be financial difficulties, because upper management thinks mid-management is more expendable, can be replaced easily, can be replaced cheaply, and/or they are protecting their jobs by saving money. They don't get rid of the guys (rank-and-file) doing the actual "dirty" work until absolutely necessary because they need them to do the "dirty" work (besides your pay could mean keeping 3 of the little guys).

Hospitals are expanding and contracting daily due to outside forces (insurance payments, medicare, etc.). So, it is possible that you didn't do anything wrong, they just can't afford you now.

Take the severance. It appears as if you might be in a good position to "negotiate" for more severance, letters of recommendation, time to find another position, etc. If possible, negotiate for an extension of them paying for your health benefits for at least 6 months. They are getting rid of you anyway so if you give them no problems, you might come out a winner.