Timothy Taylor writes,

moving back the retirement age could have a large effect in addressing the financial problems of Social Security, but would have a much smaller effect in helping Medicare.

Read the whole thing. The reason that raising the age of eligibility for Medicare does not produce a large effect is the phenomenon of “morbidity compression.” Basically, no matter how long you live, if you die a natural death, most of your health problems will be concentrated in roughly the last three years of your life. Bad problems kick in at around 72 for people who die at 75, and at 92 for people who die at 95. These days, if you make it to age 65, there is a good chance you will not have really expensive medical problems until you are in your late 70s, so raising the age of government dependency for health care does not do much to reduce Medicare’s cost.

On the other hand, however, I think that raising the age of government dependency is still a good idea. You want to get people into thinking in terms of financing the years 65-75 with their own money. That would increase labor supply and savings. Also, reducing the proportion of the population on Medicare would help to lower the political rigidity that surrounds it.