As I've argued in the past (here and here), U.S. health care spending seemed to slow down in the mid-2000s, well before any cost-constraining measures of the 2010 legislation could take effect. In addition, the slowdown in health care costss has been international, which suggests that changes in U.S. law are not the driving factor. In the December 2014 issue of Finance & Development, Benedict Clements, Sanjeev Gupta, and Baoping Shang offer more explanation on the international dimensions of health care costs in high-income countries in their article, "Bill of Health."
Here is there figure showing the pattern of health care spending across OECD countries in the last few decades. Notice that there are several times when it looks as if health care costs are slowing for a few years, before they start rising again. In discussing the recent slowdown in the rise in health care costs, they note: "The slowdown in growth for all types of spending in nearly all advanced economies—and at about the same time—suggests that it was driven by a common factor. The common element appears to be the global financial crisis, which affected economic activity and governments’ capacity to finance continued health care spending growth."
Moreover, the authors point out that the countries where the global recession hit hardest, circled in red, have had the biggest slowdown in health care costs, where the countries where the recession was weakest, circled in green, have had less of a slowdown in health care costs.
Of course, it's theoretically possible that health care spending in almost every other country was slowing down because of the recession, and short-run cuts in government health care spending, while health care spending in the U.S. was slowing down for long-run reasons driven by the 2010 legislation. But it's pretty unlikely. Indeed, when the authors project how much public health spending will rise as a percent of GDP in the next 15 years, they project that the rise will be largest of all in the U.S.--thus squeezing government budgets even further. Their predictions separate out the aging of the population, in blue, from the rest of the increase in health care spending, in green.