President Obama has spent the past two weeks on the defensive as millions of Americans are receiving cancellation notices from their insurers as a result of changes made by his health care law.

But there’s a bigger problem for Obama than Americans getting annoyed at having to lose plans that they like, despite his oft-repeated promise that they could keep them.

At the end of the day, people aren’t necessarily loyal to insurance policies or companies. Americans routinely switch plans and insurance companies as they shift jobs, move, get married or have kids.

Insurance plans are merely a means to an end — obtaining medical care.

That’s why it isn’t Obama’s repeated pledges that people could keep their health care plans that are likely to cause him the most political headaches. It’s his other promise.

As he formulated it in a 2009 speech to the American Medical Association: “[N]o matter how we reform health care, we will keep this promise: If you like your doctor, you will be able to keep your doctor. Period.”

Ultimately, if the tech problems plaguing the rollout of Obamacare are fixed, and Americans are able to obtain affordable health insurance through the law’s new exchanges that allow them to keep their doctors, the current uproar over lost insurance plans will simmer down.

But if Americans also lose their doctors, the political problems confronting the president and Obamacare will only deepen.

In the face of media reporting on the high cost of Obamacare-compliant insurance plans, defenders of the law have typically noted that the Congressional Budget Office expected them to be even more expensive.

But one of the main ways insurers contained costs was by stripping down the number of hospitals and doctors that are covered by their plans.

In New Hampshire, only one insurer — Anthem Blue Cross Blue Shield — is offering plans on the state’s insurance exchange.

And to keep costs down, Anthem included only “16 of the 26 acute general care hospitals in the state” in its network, according to the Concord Monitor.

In California, key medical centers such as Cedars-Sinai are absent from plans offered through Obamacare.

On Monday, the Wall Street Journal published an op-ed by Edie Littlefield Sundby, a cancer patient whose plan was cancelled as a result of Obamacare and who won't be able to keep her current team of doctors that she argued were essential to her survival.

In August, Modern Healthcare reported on a McKinsey & Co. analysis of 955 Obamacare plan offerings in 13 states, which found that almost half were of “the narrow-network type,” meaning enrollees' choices were restricted and that they would “have limited or no coverage if they seek care outside their plan network.”

A survey of 409 doctors by the Medical Society of the State of New York found that 44 percent weren’t participating in any health plan offered on the state’s exchange, 33.5 percent weren’t sure if they were participating in any plans and just 6.4 percent said they were participating in more than five plans.

In addition to those forced to seek insurance through exchanges, seniors could experience access problems as hospitals and other medical providers adapt to Medicare payment cuts.

This would challenge Obama to explain his statement to Medicare beneficiaries during a September 2009 health care speech to a joint session of Congress: “Don't pay attention to those scary stories about how your benefits will be cut.”

This week, the Associated Press ran a story on the costly options confronting those losing their insurance coverage under the law. The headline read: “Sticker shock often follows insurance cancellation.”

But mounting evidence suggests that when insurance plans kick in on Jan. 1, sticker shock will be followed by another phenomenon — access shock.