In many states, more than half the plans offered for sale through HealthCare.gov, the federal online marketplace, have a deductible of $3,000 or more, a New York Times review has found. Those deductibles are causing concern among Democrats — and some Republican detractors of the health law, who once pushed high-deductible health plans in the belief that consumers would be more cost-conscious if they had more of a financial stake or skin in the game.

“We could not afford the deductible,” said Kevin Fanning, 59, who lives in North Texas, near Wichita Falls. “Basically I was paying for insurance I could not afford to use.”

He dropped his policy.

As the health care law enters its third annual open enrollment period, premiums and subsidies have been one of the administration’s main selling points.

“Most Americans will find an option that costs less than $75 a month,” President Obama said.