A single payer health care system COULD be a better use of taxpayer dollars than taking care of the elderly, granted health care costs actually go down. I don't think Obamacare does anything in its current form to reduce the cost of health care, though. It's just the republican version of government health care.
I was able to sit in on a presentation by someone from The Brookings Institute on the subject, and that's basically the gist of it.
The theory is that when you go to the state level exchange, and you shop for a plan, insurance companies will compete for the business of folks who aren't getting insurance elsewhere, and the competition would drive price down. Then, as the system gains more ground and gets more solvent, more people will buy into the exchange (assuming the plans in the exchange are getting a better deal that what they're getting on their own from their employers), and then ultimately, the hope is that even the elderly can get on this instead of Medicare. That's the end game.
Will it work? I don't know. According to the think tank guy, the ACA is pretty much the sum total of about every single theory put out there about how to decrease health care costs in the last twenty years or so. They just kind of threw everything at the wall to see what would stick.