Based on the Economic Stimulus Bill as passed by Congress, persons with income from Supplemental Security Income (SSI) alone will not qualify for a tax rebate check.
The law authorizing the rebate checks (H.R. 5140) specifically limits qualifying income from Social Security benefits to "any amount received by the taxpayer by reason of entitlement to - (A) a monthly benefit under Title II of the Social Security Act, or (B) a tier 1 railroad retirement benefit."

SSI is authorized under Title XVI of the Social Security Act, not Title II.

Supplemental Security Income is funded by general tax revenues, not Social Security taxes. It is designed to help aged, blind, and disabled people, who have little or no income by providing cash to meet basic needs for food, clothing, and shelter.

Specific Questions? Call the IRS
Since everybody's tax situation is different, and final qualification for the rebate checks will be decided by the IRS based on each individual's 2007 tax return, all specific questions regarding the rebate checks should be directed to the IRS. You can call the IRS at: Toll-Free, 1-800-829-1040 Hours of Operation: Monday – Friday, 7:00 a.m. – 10:00 p.m. your local time (Alaska & Hawaii follow Pacific Time).