WASHINGTON — The nation’s health care law is approaching limits as its third sign-up season gets underway.

Enrollment on the federal and state exchanges began Sunday. President Barack Obama’s health overhaul already has reduced the uninsured rate to a historic low of about 9 percent, but the gains will be harder in 2016.

Costs are going up on the private, taxpayer-subsidized coverage sold through HealthCare.gov and state insurance exchanges. Also, many of the 10 million-plus eligible uninsured Americans tend to be younger people on tight budgets.

Others are trapped in what’s called the “Medicaid gap.” Across the South, Republican-led states have turned down the Medicaid option, leaving millions uninsured. That’s unlikely to change, with political divisions magnified in a presidential election year.

It all makes the uninsured tougher to reach.