When I applied for widows benefits a year ago, I was told...
I'm afraid Social Security is right -- you have to be 65 to be eligible for any of Medicare's programs (unless you are disabled and have been receiving Social Security Disability benefits for at least 24 months, in which case you'd be automatically enrolled). You should plan on considering which parts of Medicare to enroll in and begin filling out the paperwork three months before your 65th birthday.
There are some loopholes in Social Security that really stink. My husband was on SSDI for 3 years, and passed away recently. When I got the letter from Social Security, I answered all their questions, then was informed that I would not receive a survivor's pension until I was at least 60, I am 51. And there's no guarantee that I'll receive a survivor's pension at 60, I have to call back to see if I qualify. That's my thanks for being a 24/7 caregiver with a full time job.