Don Taylor has a three part interview (one, two, three) with Charles Blahous, "one of the two public trustees for Social Security & Medicare." On Medicare's financing problems:

Pre-2035, demography is the bigger factor.  Ultimately health cost inflation would become the larger factor.  This in my view is hugely misunderstood.  Yes, health cost inflation is a huge issue, but it’s a harder factor to predict, and it doesn’t actually become Medicare’s biggest problem for some time.  We first have to come to grips with the number of years for which individuals receive support under Medicare.