When Obamacare was being sold to the public, the president and his supporters made big promises about the law. But three years later, it looks a lot more limited. Indeed, it sometimes seems as if we're hearing more about what Obamacare won't do as what it will. Here are five things we probably shouldn't count on Obamacare to do:

It won't control health costs. A few months after the health care law passed, former White House advisers touted the law's cost controls: The law, they wrote in the New England Journal of Medicine, "puts into place virtually every cost-control reform proposed by physicians, economists, and health policy experts." Apparently it wasn't enough, even for the law's backers. A group of prominent liberal supporters of Obamacare recently launched a new effort to control health spending. The Washington Post reported that "While all support the Affordable Care Act, they tend to agree that additional legislation will be necessary to control health-care costs."

It won't lower premiums for everyone. During his first presidential campaign, Obama pitched his health care overhaul as a way to "lower premiums by up to $2,500 for a typical family per year." But average family premiums have continued to rise since Obamacare passed, insurers and actuaries are warning that they'll rise even higher as the law kicks in, and even Health and Human Services Secretary Kathleen Sebelius now says that some premiums will rise under the law. Sen. Chuck Schumer (D-NY) also seems to think the law could cause premiums to spike.

It won't reduce emergency room usage amongst the poor. One of the arguments for the law was that it would reduce emergency room utilization by giving low-income individuals Medicaid coverage that would allow them to see a doctor instead. But according to a study published this week, a randomized controlled trial found that giving individuals Medicaid does not reduce emergency room usage.

It may not make low-income Medicaid beneficiaries healthier or happier. That same study found "no significant effect of Medicaid coverage" on any of the objective physical health markers it looked at. The study looked at a very poor, very sick population, and examined health markers that should have been some of the easiest to treat. The study's authors also reported that they "did not detect a significant difference in the quality of life related to physical health or in self-reported levels of pain or happiness." Roughly half of the law's coverage expansion is projected to come via Medicaid.

It won't get rid of "uncompensated care." This is a little bit technical—but it's important. Related to the argument about emergency room usage, Obamacare supporters said the expense of the law could be justified in part by the way it would reduce uncompensated care—the "free" care hospitals give to those without insurance. The federal government was already paying hospitals for that care, the argument went, so why not just use that money to pay for insurance instead? President Obama claimed that the cost of uncompensated care was raising insurance prices nby an average of $1,000. Now it looks like the Obama administration believes that uncompensated care costs won't go down any time soon. The president implicitly admitted this when he proposed adding $360 million to a fund that pays hospitals for uncompensated care, a bump that would effectively get rid of the cuts the health law was supposed to enable.