WASHINGTON (AP) — The first stage of President Barack Obama’s health care overhaul is expected to provide coverage to about 1 million uninsured Americans by next year, according to government estimates.

That’s a small share of the uninsured, but in a shaky economy, experts say it’s notable.

Many others — more than 100 million people — are getting new benefits that improve their existing coverage.

Overall costs appear modest at this point, split among taxpayers, employers and individuals who directly benefit, although the biggest part of the health care expansion is still four years away.

For weeks, the White House has been touting the new law’s initial benefit changes, even as Obama dares Republicans to make good on their threat to repeal his signature social policy achievement. Now, a clearer picture is starting to emerge from the patchwork of press releases.

In 2014, government tax credits will help uninsured workers and their families pay premiums, and Medicaid will take in many more low-income people. Eventually, more than 30 million will gain coverage, sharply reducing the number of uninsured and putting the nation on a path to coverage for all citizens and legal immigrants.

Political salesmanship and an attempt to address some glaring health insurance problems are key elements of the strategy to explain the initial changes resulting from the law. After battling for a year to pass the legislation, Democrats desperately wanted to have tangible accomplishments to point to in high-stakes congressional elections this fall. But they also have to deflect lingering questions, often stirred up by opposition candidates, and doubts about the effectiveness of the overhaul and its costs.

“We’ve seen increasing numbers of people losing their health insurance, particularly in this recession,” said Sara Collins, vice president of the Commonwealth Fund, a New York-based health research clearinghouse. “Providing this early relief will help people who are particularly affected by the downturn.” Collins reviewed coverage estimates in federal regulations for The Associated Press.

Among the beneficiaries will be many people locked out of insurance because of medical problems.

The Raether family of suburban Milwaukee will gain from two of the changes: Elimination of lifetime coverage limits and a ban on insurers turning away children in poor health.

Four-year-old daughter Mira, who was born prematurely and has kidney problems, exhausted the lifetime limit on her parents’ policy earlier this year. Mira now has temporary Medicare coverage because of a kidney transplant, but her parents were worried about what would happen when they have to get her back on private insurance.

“A huge weight has been lifted,” said Sheryl Raether, the mother. “She has ongoing health care needs, and I was afraid she’d hit another lifetime limit.” Medicare not only covers seniors, but people of any age with permanent kidney failure.

The major early coverage benefits include:

— Allowing young adults to stay on their parents’ coverage until they turn 26. In 2011, an estimated 650,000 young people who would otherwise have been uninsured will gain coverage. Another 600,000 will benefit by switching from individually purchased policies to less costly, more comprehensive employer plans. The number with coverage will grow in 2012 and 2013.

—A health plan for uninsured people with pre-existing health conditions. From 200,000 to 400,000 could benefit in 2011, according to the Congressional Budget Office. The government may limit enrollment if $5 billion allocated through 2013 starts to run out, as projected. Beginning in 2014, insurers will be required to accept all applicants, regardless of medical history.

—Ending lifetime limits on coverage, and restricting annual limits. As many as 20,400 people a year hit lifetime limits, as did Mira Raether. Many more — an estimated 102 million — are in plans that impose such limits and will no longer be able to do so.

— Requiring insurers to cover children with medical problems. An estimated 51,000 uninsured children are expected to gain coverage. Another 90,000 children who have been excluded for coverage for a particular condition — asthma, for example — will also benefit.

Many Americans covered through employers won’t see the changes until Jan. 1, the start of their next health plan year. That means 2011 will be the first year that the early benefits are fully in place.

What that entails for costs is a matter of intense speculation. A recent survey of employers by Mercer, a major benefits consultant, found that 42 percent expect an increase of 2 percent or less, while one-fourth expect an increase of 3 percent or more. Government estimates are generally lower.

Beth Umland, research director for Mercer, said employers were expecting health cost increases averaging about 6 percent a year before the law. “Now they are looking at an additional 2 or 3 points, so that 6 percent can become a 9 percent, and that seems to be above their comfort level,” she said.

Dave Osterndorf, chief health actuary for the Towers Watson consulting firm, said large employers will respond by passing on costs to their workers. “These first few changes, in and of themselves, will not dramatically change the way employers look at the provision of health benefits,” he said. “Employers will feel part of the impact, and employees will feel part.”

Some coverage gains may take a while to add up. For example, Blue Cross Blue Shield Kansas City reports brisk sales to small businesses by advertising Obama’s new tax credit for those who offer coverage. CEO Tom Bowser said more than 60 of the 227 small firms signed up so far did not previously offer health benefits.

“Small groups are one of the toughest markets we have,” said Bowser. “Because of the economy, more and more were dropping coverage entirely, and we’ve able to reverse that.”