Supporters of the new law have argued that states will benefit from efforts to slow health care inflation and billions of dollars in new federal spending on subsidies for the uninsured and on an array of programs like community health centers.

But even with more federal help, the challenge for states like Alabama, Arkansas and Texas that now offer only limited Medicaid coverage will be substantial. In these states, Medicaid has been mostly restricted to low-income families with children, pregnant women, certain people with disabilities and some elderly. The income cutoffs have also been extremely low.

Beginning in 2014, however, anyone with an income of up to 133 percent of the federal poverty level, or $29,300 for families of four, will be eligible for coverage under Medicaid. For the first three years, the federal government will pick up the entire cost of these new enrollees, but the state share then gradually increases until it reaches 10 percent in 2020.

Texas, which has some of the most restrictive Medicaid eligibility rules in the country for adults, currently covers working parents only if they do not earn more than roughly 20 percent of the federal poverty level. The program does not cover childless adults.

Anne Dunkelberg, associate director of the Center for Public Policy Priorities, a research group in Austin that strongly supported the health care law, estimated that if the legislation went into effect today, an additional one million adults would qualify for Medicaid, at a cost of $370 million a year if Texas were to pay its full 10 percent share.

In addition, Ms. Dunkelberg said, many children who are currently eligible but are not enrolled in Medicaid and the state Children’s Health Insurance Program will emerge and want to join, potentially costing the state several hundred million dollars.

Some states, like Arizona, face an immediate fiscal conundrum because of stipulations in the law that prohibit them from rolling back their existing Medicaid programs before the required expansion takes effect.