President Obama will try to allay anxiety over his signature health-care law Friday during a visit to California, a state that the White House is highlighting as proof that the law is working.

(Jessica Rinaldi/Reuters)

With the focus in recent months on the law’s shaky rollout and continuing political battles, the president wants to draw attention to a state that has embraced the law and yielded some good news: Officials in the Democrat-led state recently released figures that show insurers expect to charge lower-than-expected premiums for individual policies sold under the law.

On the eve of his comments, however, a different story emerged from Ohio. Officials in the Republican-led administration Thursday released details about rates proposed by insurers there, estimating that they represented an 88 percent increase in the cost of coverage that would likely lead to a substantial increase in premiums.

“We have warned of these increases,” Ohio Lt. Gov. Mary Taylor (R) said in a statement. “The Department’s initial analysis of the proposed rates show consumers will have fewer choices and pay much higher premiums for their health insurance starting in 2014.”

The competing narratives illustrate the deep political divide that colors virtually every aspect of the health law three years after its passage and the difficult task Obama faces as he seeks to promote it a few months before its key provisions kick in.

Obama’s comments in San Jose, to be delivered while the president is on a fundraising swing, come as the administration is ramping up efforts to promote the law, which faces a major test this fall. The health insurance “exchanges” are supposed to open for business Oct. 1. These exchanges are designed to be online marketplaces where people can find and compare plans and get government subsidies for their purchases.

Seventeen states, including California, are setting up their own exchanges, as was intended by the law. But 27 states, most of them Republican-led, have left the task to the federal government, saddling the administration with an enormous and unexpected job. The rest of the states will form partnerships with the federal government to create the exchanges.

Further complicating the administration’s efforts are the number of states that have rejected the law’s expansion of Medicaid, the state-federal health program for the poor and disabled. The law called for a substantial broadening of Medicaid — which would put the administration more than halfway toward its goal of extending coverage to 30 million Americans over the next 10 years. But more than a dozen states, all Republican-led, are refusing to expand Medicaid.

Ohio is among the states taking a different tack than California. It has declined to set up its own exchange, letting the federal government set one up instead, and Republicans there remain divided over whether to expand Medicaid. It is the first Republican administration to release the rates being requested by insurers on its exchange.

California, by contrast, has long been a leader in implementing the law. It was the first state to create a health exchange under the law and is among the 23 states committed to expanding Medicaid.

“I don’t think the Affordable Care Act can succeed unless it succeeds in California,” Drew Altman, president of the nonpartisan Kaiser Family Foundation, said. “It’s not often we’re saying as goes California, so goes the nation. But it’s true this time.”

Of the 2.7 million young and healthy people the White House wants to sign up for insurance next year, one-third live in Texas, Florida and California. Altogether, California has 7 million uninsured people, the highest number in the country.

Covered California, the state agency implementing the law, last month announced that 13 plans would be available on its exchange and that the average monthly premium would be about $321. That is significantly lower than predicted by the Congressional Budget Office when the law was passed in 2010, and for most people, the cost will be at least partly offset by subsidies.

The state has not released an estimate of how the proposed rates compare with current rates. The law’s supporters say even if the new plans are more expensive, it is because they offer better benefits than the old plans.

But some insurance experts have warned that healthy males in their 20s are likely to face higher costs. And people with existing, bare-bones private plans could see their rates jump. In Ohio, for example, one plan now costs as little as about $30 a month, according to Ohio officials.

In California, officials say they aggressively negotiated with insurers to keep the rates low. They also said that competition among the insurers is holding rates down.

If healthy people choose to skip coverage and instead pay the mandated tax penalty, it could hurt the government’s efforts to bring enough healthy people into the insurance pool. Those healthy people are needed to offset the cost of sick people; insurers are expecting an influx of them.

While California has touted the rates proposed by insurers, some say the news is not all good. Some large national insurance companies, including Aetna and UnitedHealth, are not offering plans on the state exchange. And many of the plans on the exchange offer a narrow choice of doctors and hospitals.

Some experts say the political atmosphere is casting a shadow over each state’s reaction to the insurance rates.

“Ohio is too upset, and California is too happy,” said Micah Weinberg, senior policy adviser to the Bay Area Council, a business group that supports the health law.

“I suppose the question is, are we finally getting a release without spin, or are we getting Republican spin?” said Robert Laszewski, a health-care consultant and former insurance executive. “Like California, we are getting the data they want us to see.”

CORRECTION: A prior version of this article said that Ohio officials on Thursday released rates proposed by insurers for plans to be sold on the Ohio exchange. The state released insurers’ estimates of their increased costs of providing coverage, and state officials said premium rates likely would track closely.