President Obama’s health care law was supposed to expand choice for consumers. But with just weeks to go before open enrollment begins on the law’s subsidized insurance exchanges, it’s increasingly looking like the array of plans and providers being offered will fall short of the program’s ambitions.

In New Hampshire, for instance, Anthem Blue Cross Blue Shield is the only insurer offering coverage on the state’s exchange. Even more strikingly, the plans it will be selling through the exchange will have a relatively limited provider network.

The Concord Monitor reports, “By contracting with 16 of the 26 acute general care hospitals in the state, Anthem was able to keep premium costs 25 percent lower than they would be if all hospitals in the state were part of the network, according to a statement from the insurer.”

On Thursday, Michael B. Green, president and CEO of Concord Hospital, explained why his hospital network wasn’t participating in Anthem’s Obamacare plans.

“Our decision to not participate in this exchange at this time was not a political statement,” he wrote in the Concord Monitor. “We are not opposed to the tenets of the Affordable Care Act or exchanges. However, Anthem was unwilling to negotiate sustainable contract terms, and the reimbursement rates that they offered would ultimately result in us being paid less than what it costs us to provide care.”

For the past several months, a lot of the Obamacare debate has focused on “rate shock” – that is, the fact the health care law’s regulations will increase the price of insurance coverage, particularly on younger and healthier Americans. But this debate has obscured another important issue – “access shock.”

New York Times Columnist Paul Krugman, decrying the lack of serious policy wonks on the right, wrote this week that “we now have a good idea what insurance premiums will be once the law goes fully into effect; a comprehensive survey by the Kaiser Family Foundation finds that on average premiums will be significantly lower than those predicted by the Congressional Budget Office when the law was passed.”

There are a number of responses to this. The most obvious is that lower than expected isn’t the same as being actually lower. In fact, there’s a ton of evidence that rates will be higher under Obamacare for many groups, especially for younger and healthier Americans. But to the extent that Obamacare’s insurance plans are cheaper than expected, a big reason why is that they are restricting access to many providers.

This issue generated some attention in May when California released details of plans to be offered on the exchanges with some key medical centers, such as Cedars-Sinai, absent. As the Los Angeles Times reported, the state’s largest insurer, Kaiser Permanente, came in with premiums much higher than other insurers on the exchange. The company said the reason was that it offered a more extensive range of doctors and hospitals.

Now, it’s becoming clear that this has become a broader national trend.

“Nearly half the exchange plans in 13 states with early filings will be of the narrow-network type, according to an unpublished McKinsey & Co. analysis of 955 plan offerings,” Modern Healthcare reported last month. “Enrollees in such plans will have limited or no coverage if they seek care outside their plan network. In exchange, subscribers will enjoy lower premiums than they would pay for plans with broader networks, insurers say.”

The article continued, “Insurers including Aetna and Health Net say narrower networks, made up of hospitals and physicians selected using cost and patient-outcomes criteria, are necessary to keep their exchange plan premiums affordable while still meeting the requirements of the Patient Protection and Affordable Care Act.”

In other words, Obamacare drives up the cost of premiums by requiring companies to cover those with pre-existing conditions, to pay for a number of designated benefits and to limit out-of-pocket spending. So to keep rates in check, insurers are paring down their networks.

This means that a beneficiary may have an insurance policy that theoretically covers a medical service, but could have a tough time finding an appointment or a facility that can provide the service.

Modern Healthcare raises another potential issue: “There also are concerns that narrow-network plans will cause risk-selection problems in the exchanges because lower-priced plans with smaller networks are likely to attract younger, healthier enrollees and drive people with serious health conditions into plans with wider networks. That could force all plans to pare down their networks to survive, thus limiting consumer choice. Then regulators might have to step in.”

Interestingly, one of the arguments that supporters of the health care law have consistently made is that even though Obamacare may make health insurance more expensive in some cases, people will be getting better, more comprehensive policies. But the limitations on access undercut this point.

The response to this, I suppose, would be that somebody who would otherwise be uninsured is still far better off having insurance, even if there are restrictions on its use.

However, it’s also worth keeping in mind that this isn’t the only way that the health care law may affect access. Paul Spitalnic, the acting chief actuary of the Centers for Medicare and Medicaid Services, has warned that the law’s cuts to Medicare payment rates could restrict access for the program’s beneficiaries.

Additionally, if the capacity of the nation’s health care system doesn’t increase to meet the demands of the millions of newly-covered Americans flooding providers, then everybody may be experiencing access shock in the form of difficulty making appointments or longer waits at doctors’ offices.