Social Security Disability Insurance (SSDI) not Supplemental Security Income (SSI). SSI goes to Medicaid. Medicare eligibility begins at age 65 for Retirement and Survivors Insurance (RSI).
Disabled beneficiaries under age 65 who have been receiving Social Security disability benefits for more than 24 months
If you have been receiving (or have been entitled to receive) Social Security disability benefits for at least 24 months (not necessarily consecutively), you may be eligible to enroll in Medicare. To enroll, you must be entitled to benefits in one of the following categories:
You are disabled, of any age and receiving worker’s disability benefits
You are a disabled widow or widower age 50 or older, or
You are a disabled beneficiary who is older than age 18 who receives benefits based on a disability that occurred before age 22
http://medicare.org/index.php/medicare-program/benefits-for-disabled.html