There's something of a tug-of-war between right and left as to whether our aging population, or growing healthcare costs, are the major problem with Medicare's financial sustainability.  The answer is that in the short term, it's the former; in the long-term, the latter.  But as Arnold Kling points out, the fact that Medicare exists is why we worry about sustainability:

From my perspective, the health care cost issue is a bit of a red herring. If you had government out of the health care financing business, you would not worry about what health care costs are doing. If my fellow citizens choose to spend more of their money on their health care, that's not my concern. It's the prospect of my fellow citizens spending more of my money on their health care that has me worried.

More broadly, as long as the government is in charge of providing healthcare to the elderly, population aging will help drive healthcare costs higher.  For retirees, availability of healthcare is one of two or three major issues that they vote on.  Since they pay relatively little in taxes, their desire is for unrestrained spending on healthcare, and because they are one of the nation's most powerful voting blocs (arguably, they are the most powerful voting bloc), the aging of the population, combined with government funded healthcare, will keep the rate of healthcare cost inflation high.