Paul Fronstin, an economist at the Employee Benefit Research Institute, a nonpartisan organization, said the proposal would work only if Mr. Romney made additional efforts to bring down the cost of health care. In the past, he said, advocates of such proposals typically offered tax credits ranging from about $1,500 to $2,500 a year for an individual — not necessarily enough to make coverage affordable.

“Will other things bring down premiums to make those tax credits more meaningful?” Mr. Fronstin asked. “That’s an open question.”

The new health care law prohibits insurers from turning people away or charging them more because they are sick, and Mr. Romney says he will guarantee access to insurance for people with pre-existing conditions. But his guarantee would extend only to people who have maintained coverage without a significant gap. That means millions could still be rejected.

Mr. Romney says many of them could get coverage through health plans known as high-risk pools. Many states have such pools, but the coverage they offer can be prohibitively expensive.

If Obama Wins

If Mr. Obama is re-elected, he would step up efforts to carry out the health care law. Given the controversy over the law and the logistical challenge of setting up state insurance “exchanges” where people can shop for coverage, the transition will probably be rocky. But many doctors, hospitals and insurance companies are determined to make it work.

On Jan. 1, 2014, the requirement that most Americans have medical coverage takes effect. Private health plans will start enrolling people in October 2013. The result, according to the Congressional Budget Office, is that 30 million uninsured people will eventually gain coverage. To help them afford it, the federal government would subsidize private insurance premiums for people with incomes up to four times the federal poverty level ($92,200 for a family of four). And it would expand Medicaid to cover more poor people, including many adults without children.

Mr. Obama and Democrats in Congress have beaten back efforts to change the law before its major provisions take effect. But after the election, Congress will be under intense pressure to rein in deficits and debt, and lawmakers will focus anew on the costs of Medicare, Medicaid and the new health care law, which together could account for one-third of all federal spending in 2022.