In a speech on the White House lawn yesterday, President Obama essentially declared victory on Obamacare. But this victory will be tough to sustain.

Going forward, the law presents major challenges for the president and his party. Although conservatives played a role in generating some of its core ideas, the law in its final form is a strictly Democratic creation—written, passed, and implemented by a single party. In passing the law, and in billing it as an all-things-to-everyone transformation of the entire health system, Democrats shackled themselves not only to the law's specific fortunes, but to the fortunes of the entire American health system. Democrats own health care in America now, and all of its problems with it.

The foremost of these problems is rising costs. There are two ways to think about health care costs: One is at the national level; the other is at the individual level. At the national level, Obamacare's supporters frequently note that health care cost growth has slowed dramatically since President Obama took office; therefore, Obamacare's various payment reforms must be the cause. (President Obama referenced this idea in his speech yesterday.)

This claim is highly contested. It's true that the growth of health spending has slowed, but the slowdown started long before Obamacare took effect. And the additional post-Obamacare slowdown likely has much more to do with the recession than with the early effects of any of Obamacare's supposed cost-savers. That's the conclusion of analysts at the Kaiser Family Foundation, as well as the actuaries at the Centers for Medicare and Medicaid Services. It's possible this could change in the future, but it's far too early to give Obamacare credit.

Either way, this argument only goes so far. When most Americans hear about health care's rising costs, they're not thinking about the rate of growth of national health expenditures. They're thinking about their own pocketbooks and bank accounts. How much does health care cost them, personally, in terms of premiums and out-of-pocket spending?

Obamacare's supporters have a number of go-to responses when this issue comes up. Like President Obama in his speech yesterday, they often tell personal stories of individuals whose premiums were reduced under the law, making the point that in some cases, premiums will go down. But those individual stories usually come with an admission that, on average, premium costs will continue to rise even as the health law settles into place. However, the argument usually continues, premiums will rise at a slower rate than before the law was in place. "Premiums are still rising for families who have insurance," President Obama said yesterday. "But, so far, those premiums have risen more slowly since the Affordable Care Act passed than at any time in the past 50 years."

There are two problems with the line of argument. The first is that rising premiums—whether they're rising slower or not—aren't what was promised. Not only did the president specifically promise on the campaign trail that his health care reform plan would lower premiums for families by $2,500 on average; the White House repeatedly touted lower premiums for families as a primary feature of the law. "Objective analysis shows reform will help small businesses, lower premiums for American families," reads the headline of a November 2009 post at the White House blog. "CBO confirms families will save money under health reform," reads another. CBO's analysis, the post notes, didn't even account for the health law's "measures to control costs…so if anything it understates the positive impacts of reform." Americans were not promised a law that slowed the rise of premiums. They were promised a law that would lower premiums and save them money.

The second problem is that, at least in the individual market that Obamacare affects most directly, we don't even know what premiums will look like next year, or the year after that. Insurers have to submit next year's rates in the next few months, and in some cases, because so many people signed up at the last minute, they will have to do so with very little actuarial data on the health status of those getting insurance through the exchanges. Rates are going to go up. It's possible, as insurers have already quietly warned, that they might go up by a lot.

If that happens, it will be Democrats' problem.

Cost isn't the only issue that Democrats will have to contend with either.

There's also the issue of access. About 70 percent of plans offered through the law are tightly restricted, narrow networks, according to a McKinsey & Co. study. That's going to be an issue. When people with individual insurance, or Medicaid, can't see the doctors they want to see, or visit the top hospital for their disease, or can't get the procedures or drugs they want because it's not covered by their plan, or because reimbursement rates are low, that's going to be a problem for Democrats too. We're already seeing early rumbles to this effect.

To some extent, the health law's supporters will be able to divert blame onto insurance companies. But that won't work as well as it used to, because Democrats are now effectively partners with the insurance industry in the operation of the health law, and because President Obama promised that no one would lose access to a provider he or she liked. Blame that used to fall squarely on health plans will now be spread amongst the political architects of the health law as well.

The administration is already aware of this problem and has proposed rules to mitigate it by limiting the options for health plans seeking to create narrow network plans. But it's not that easy. Narrow network plans flourished on the exchanges because they are cheaper. Broader provider networks will mean higher costs. Balancing between the two in a way that is sustainable, effective, and broadly popular will be extremely difficult.

These are difficult health policy problems. They are also significant political problems. The health law has never been popular, and it is dragging down Democrats' prospects at the polls this November. Improving Obamacare's design will be difficult for even the most committed technocrat under any circumstances. But Democrats will have to do it while fighting to maintaining the legislative—and, come 2016, administrative—control necessary to steer it in their preferred direction.

Thanks to the administration's numerous executive tweaks and patches, we've already had a taste of what that will probably be like: changes made for short-term political gain that undermine the law's longer-term prospects.

All this will take place against the backdrop of a broader sense that with Obamacare, Democrats were supposed to have fixed the major problems with the American health system. President Obama pushed back against this notion yesterday, cautioning that the success of the law "doesn't mean that all the problems in health care have been fixed forever." That he felt the need to try to temper expectations suggests that he knows that those expectations are impossibly high.

When building Obamacare, liberal health wonks often referred to the law's design as a "three-legged stool"—regulations, subsidies, and a mandate. With Obamacare's design phase over, and its upkeep and adjustment period just beginning, Democrats will have to try to find a way to balance between a different trio of concerns: cost, access, and political viability. It's the three-legged stool of Obamacare maintenance—and it may be harder to support than Democrats expect.