I think everyone has already linked to CBPP's piece on the effects of raising the Medicare minimum age from 65 to 67 already, but just to add in my two cents: the key context for all of this is that what people call a long-term budget problem is really only an artifact of the long-term health care costs problem.
As long as health care costs (and, as the popular ages, demand for services) continue to spiral up, it's going to create huge problems. That's true if the problems are mainly found in government budgets, or in the private market. After all, if you completely eliminated Medicare or any other form of government-subsidized health care, you would no longer have a federal budget problem...but the economy isn't going to be very happy if seniors stop buying whatever they are currently buying and rapidly blow their savings on health care. Or, as CBPP points out, if companies go broke paying for retiree health benefits.
The bottom line is that unlike a real budget problem, which could be solved by either cutting spending or raising taxes, the problem here is a broader economic problem, and it calls for a broader economic solution. That was the point of all the cost-control efforts in ACA, and believe it or not there are some hopeful signs that perhaps it's going to work. Of course, maybe it won't. The point is that cost-shifting away from the government ("cutting spending") which absolutely can work to solve purely budgetary problems just won't work in this case.