Two years ago, New York enacted a law designed to reduce “surprise billing,” or big out-of-health-insurance-network medical bills often associated with emergency room treatment.

Now, even as the battle over repealing and replacing Obamacare rages on in Washington, D.C., other states have followed New York's lead, enacting or considering proposals addressing unexpectedly large bills that patients receive from providers who are outside their health insurer's network, often at in-network hospitals.

Nearly a third of privately insured Americans had received a surprise medical bill within the past two years, according to a 2015 Consumers Union poll. In 2014, the New York state Department of Financial Services named it a top complaint from consumers.