Currently, a person receiving Social Security disability benefits must wait 24 months (29 months after the date determined they became disabled) to receive Medicare. COBRA coverage has been the stop-gap since 1986, but in reality, hardly anyone can afford to pay COBRA for 2 years, especially those that are disabled and cannot work. Thus, even once your found disabled by SSA, you could still be within your 2 year time period and unable to afford medical care. This of course means that many times you will be unable to get appropriate treatment, which in some cases may lead to you no longer being disabled!
While of course costs for Medicare would go up if the rolls were opened to every person who is disabled, any change may result in a reduction in Medicaid spending. Further, with all the current discussions on Universal Healthcare, the costs of SSA, and the disability process, this issue has not escaped the notice of some in Congress.
By removing the 2 year wait period, we would be taking more stress off the shoulders of those already facing financial difficulties and serious life changing medical conditions. We could be helping some get proper medical care, which in turn could mean better treatment and a return to work.
For more information (with statistics) see S. Guterman and H. Drake, The Long Wait: The Impact of Delaying Medicare Coverage for People with Disabilities, The Commonwealth Fund, May 2009.