At his press conference Tuesday, President Obama assured Americans that, “To the 85-90 percent of Americans who already have health insurance: They’re already experiencing most of the benefits of the Affordable Care Act even if they don’t know it.”

Those benefits apparently include higher premiums. According to the Wall Street Journal, insurers are warning that premiums in the individual and small-group markets could double in the next few years. Already, they are well on their way. For example, California health insurers are proposing increases for some customers of 20 percent or more: 26 percent by Blue Cross, 22 percent by Aetna, and 20 percent by Blue Shield. In Maryland, Care First, the state’s largest insurer, has proposed a 25 percent increase for next year.

Younger and healthier Americans can expect to pay even more. According to a survey by the American Action Forum, healthy young people in the individual or small-group insurance markets can look forward to rate increases averaging as much as 169 percent.

While it is always difficult to pin down the exact reason for premium increases, a large portion is traceable to the new health care law. According to a recent study by the American Society of Actuaries, Obamacare will increase health insurance claims costs by 32 percent because of increased adverse selection in the insurance pool. That is, the law’s prohibition on medical underwriting will bring more older and sicker people into the insurance pool, while higher premiums will encourage the young and healthy to forgo insurance until they get sick. (The penalty under Obamacare’s individual mandate is low enough so that it will generally be cheaper for healthy people to “pay,” rather than “play.”)

In addition, Obamacare requires all health insurance plans to provide more benefits and have lower deductibles and co-payments than they do today. Not to worry, say the law’s supporters, people may be paying more but they will have better insurance — whether they like it or not. As Secretary Sebelius puts it, “These folks will be moving into a really fully insured product for the first time, and so there may be a higher cost associated with getting into that market.” In fact, a recent study of more than 11,000 plans on the individual market found that less than 2 percent of existing plans are fully in compliance with the law’s benefit requirements.

No doubt the new insurance will be more comprehensive, required to cover such things as drug and alcohol rehabilitation and contraceptives, but one does recall that the president once promised, “If you like your health care plan, you’ll be able to keep your health care plan, period.” Apparently not. Current plans are technically grandfathered in, allowing people to keep them for now, though any change in the plans requires that their coverage be brought into compliance. Moreover, because non-compliant plans cannot enroll new members, most of the existing plans will eventually disappear. Just another benefit that the American people aren’t aware of.

Americans may also not know that it may soon become harder to continue seeing the doctor of their choice. A recent survey of physicians conducted by Deloitte found that 59 percent of them expect some of their colleagues, fearing reduced payments and increased government interference in their practice, to retire early as a result of the health care law, and that others will scale back their hours.

No doubt Americans are also failing to appreciate the more than $1 trillion in new taxes over the next 10 years that were put in place to finance the new law. If they don’t understand it yet, they will soon: many of those taxes kick in this year. Of course, since the law will also add at least $1.5 trillion to the national debt over the next 10 years, taxpayers will have many future opportunities to understand the benefits of higher taxes.

Then again, maybe Americans understand more than the president thinks. This week the Kaiser Foundation released a new poll, showing that just 35 percent of Americans approve of the law.

Once again, President Obama may have underestimated the intelligence of the American people.

Michael D. Tanner is a senior fellow at the Cato Institute.