Is your retirement age 66? if so, wait until them to collect the full amount.
You're talking Social Security not Medicare, you can start SS at age 62 with reduced payments all the way out to age 70 with bonus payments added to your base rate. Medicare starts at age 65 period.
My advice, check with your employer's insurance carrier, they may automatically drop you when you turn 65 leaving you w/o health insurance coverage of any kind. Previous post suggested starting six months early, I don't think there is much you can do until you are down to about 90 days.
I retired early and my wife carried the insurance. When she retired they dropped her back from a family plan to single coverage and I paid a grand a month to bring it back up to a family plan. When I turned 65, they dropped me completely and I transitioned to Medicare w/ a supplemental policy to caulk the leaks. They would not carry me past 65. My wife is 63 and still covered by her former employer's health plan as part of her retirement benefits which will end at age 65. Hope this helps clarify things for you.
Regards,
GtG
PS Maybe if you are a member of the UAW/CIO you might get lifetime coverage in you retirement package (or a congress critter, GS-15, or such like), but us peons get the one size fits all coverage. Even retired military get "Tri Care for Life" which is a slightly beefed up medicare.