WASHINGTON – Less than a year before Americans will be required to have insurance under President Barack Obama’s health-care law, many of its backers are growing increasingly anxious that premiums could jump, driven up by the legislation itself.

Higher premiums could undermine a core promise of the Affordable Care Act: to make basic health protections available to all Americans for the first time. Major rate increases also threaten to cause a backlash just as the law is supposed to deliver many key benefits Obama promised when he signed it in 2010.

“The single biggest issue we face now is affordability,” said Jill Zorn, senior program officer at the Universal Health Care Foundation of Connecticut, a consumer advocacy group that championed the new law.