SACRAMENTO — Swan Lockett had high hopes that President Obama’s health overhaul would lead her family in Texas to an affordable insurance plan, but that hasn’t happened.
Instead, because lawmakers in her state refused to expand Medicaid, the 46-year-old mother of four uses home remedies or pays $75 to see a doctor when she has an asthma attack.
‘‘If I don’t have the money, I just let it go on its own,’’ Lockett said.
The federal health care overhaul has provided coverage for millions of Americans, but it has only chipped away at one of its core goals: to sharply reduce the number of people without insurance.
Obama said last week that 8 million people have signed up for coverage through new insurance exchanges, but barriers persist, blocking tens of millions of people around the nation from accessing health care.
Questions of eligibility, immigrant coverage, and the response from employers and state legislatures mean considerable work lies ahead for health care advocates and officials, but cost remains a particularly high hurdle for low-income people who are most likely to be uninsured.
‘‘We think that most people will get insurance once it’s affordable to them,’’ said Cheryl Fish-Parcham of Families USA, a health advocacy group.
There are myriad ways people fall into coverage gaps. Some are eligible for discounted policies but say they still can’t afford their share of exchange plans.
Others earn too much for subsidies. Immigrants living in the country illegally can’t obtain care under the law. Dozens of states haven’t expanded Medicaid. And some employers have reduced staff hours to avoid being forced to provide care.
‘‘I’m a nurse, but my employer doesn’t offer health insurance,’’ said Gwen Eliezer, 32, who lives north of Asheville, N.C.
Eliezer works an average of 29 hours a week at a nursing home, so her employer isn’t required to cover her. She qualifies for a subsidy but says the plan she found with a $200 monthly premium and $6,500 deductible is too expensive. So while her 6-year-old son qualified for Medicaid during open enrollment, she goes without. She pays cash to see a doctor for gastrointestinal pain but says she can’t afford to get the problem diagnosed.
‘‘If I went through an emergency room, I can claim acute pain,’’ she said. ‘‘But then I’d end up with a lot of debt to a hospital.’’
Before the launch of the Affordable Care Act, about 48 million people, or 15 percent of the population, went without health insurance, according to the Census Bureau. The number of people recently enrolled includes those who switched from previous plans, and it isn’t clear how many previously uninsured people are now covered.
The share of adults without insurance shrank from 17.1 percent at the end of last year to 15.6 percent for the first three months of 2014, according to a Gallup-Healthways Well-Being Index released this month. The decline would translate to about 3.5 million people gaining coverage, according to the study.