President Barack Obama said Friday that there are enough enrollees in the marketplaces for his signature health care law for the private insurance exchanges to be successful.

In an interview with WebMD’s Lisa Zamosky, the President noted that his administration announced this week that 4.2 million people have enrolled in the Affordable Care Act exchanges, saying the figure “is already large enough that I’m confident the program will be stable.” The exchanges require a delicate demographic balance, with enough young and healthy customers to subsidize older, sicker enrollees. Data released by the Department of Health and Human Services this week showed that enrollment by young people has lagged administration targets.

Obama also admitted that some Americans may end up having to change their healthcare providers in order to save money under the law, an apparent walk-back from his pledge that “if you like your doctor you can keep your doctor.”

“For the average person, many folks who don’t have health insurance initially, they’re going to have to make some choices,” Obama said. “They might end up having to switch doctors, in part because they’re saving money. But that’s true if your employer suddenly decides that we think this network is going to give a better deal.”

Obama also defended the law from criticism that it is raising employer-provided coverage premiums, saying premiums were rising well before the law was passed. He added that the law is helping to slow the pace of growth.

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