The ratio of MM (Medicare and Medicaid) spending to GDP can be broken into the ratio of MM to total health care spending (HC) and the ratio of HC to GDP:
MM/GDP = (MM/HC)*(HC/GDP)
The reason that MM/HC has been rising is largely demographics--more old people, living longer. The reason that HC/GDP has been rising is that health care is that, as Robert Fogel puts it, we are approaching saturation with consumer goods, so now all that's left to want more of is education, health care, and leisure.
Going forward, the right way to forecast the ratio of MM to GDP is to forecast the path for the two components. At most, you could have each component asymptotically approach one.
So, extrapolating a trend is not a good way to make a forecast.
Having made that point, I agree nonetheless that the ratio of MM to GDP bears watching. See The Great Race.
My solution to the problem is to get control of the ratio of MM/HC by raising the age of eligibility for Medicare. In the most extreme case, we could Phase out Medicare.
Hamilton has a different approach.
Rather than vote on what benefits they want to cover, let Congress vote each year on how much money to spend. That means Congress exchanging the rich uncle role for one it which it says, "we'll help with what we can afford, but you're responsible for the rest." Let the debates each year be over just how generous a dollar payment Congress is willing to provide, rather than who can come up with the longest list of goodies.
In other words, he wants to change the welfare state from a defined-benefit plan to a defined-contribution plan, where the relationship between benefits and contributions is determined by the reality that government is a tax-and-transfer institution, not a savings institution.
A less wonkish approach would be a balanced budget amendment that includes entitlement spending. Have we reached the point where the benefits of such an amendment exceed the costs in terms of fiscal flexibility?