The short answer is...
Not Likely!
It is a common misconception that once you reach 65 Medicare will be there to get you through any long term care crisis you may encounter. It is true that Medicare was designed to provide medical services to senior citizens. However, there are definite restrictions on how long you can receive services. There are also limits on the types of services you can receive.
With long term private care insurance though, you are far more likely to find that your insurance will cover a wider range of services and definitely for a longer period.
Check out the government's
Medicare site to look in to Medicare restrictions. Do this before you need the services too.