WellPoint Inc. Chief Executive Angela Braly is facing her biggest test yet as the nation’s largest health insurer comes under fire for its plans to raise rates as much as 39% in California.

So far, Ms. Braly has chosen to fight back. Instead of issuing a Toyota-style apology, she is turning her critics’ argument around, citing rising health-care costs driven by doctors and hospitals, which she says aren’t addressed by the current health-overhaul bills.

The strategy, on display last week during a contentious House hearing focused on the rate increase, could get another airing Wednesday, when Ms. Braly and other top health-insurance executives are expected to appear before the Obama administration’s top health official to discuss health-care premiums.

As the company’s challenges stretch beyond Washington¿ state officials and lawmakers are raising questions about its rate increases in Maine, Connecticut and Colorado, as well as California¿her strategy is playing well with investors.

WellPoint’s shares had slipped when news of the rate increases broke, but the stock gained almost 2% on the day Ms. Braly testified in Congress, and it is up 115% from the low it hit last March.

Investors said they are relieved that the company is standing by the increases. Without them, Ms. Braly argues, the company can’t break even in the risky business of selling insurance to individuals, which has become more difficult as the economy has caused healthier people to forgo buying the policies.

But Ms. Braly has also gotten some questions from company directors about the rate-increase decision, including whether it could have been timed differently, says a board member.

Larry Glasscock, who stepped down as the board’s chairman on Monday, said, “she’s responded to those questions and the board is fully aware of why [the increases] were necessary.”

Like other health plans, WellPoint’s rolls are falling as more companies lay off workers and cancel health benefits. It can’t afford to price itself out of the individual market. WellPoint’s enrollment in commercial risk products, which include individual insurance, declined to 12.5 million at year-end from 14.2 million in 2006, according to Goldman Sachs.

WellPoint has also been squeezed by a rise in recipients of Cobra, a federal program that allows people who have lost their jobs to keep their insurance. Cobra members tend to be sicker and use more benefits.

But Ms. Braly’s combative approach risks making WellPoint even more of a lightning rod for Democrats at the federal and state levels who are eager to channel consumer anger at insurance rates and to generate momentum for health-overhaul legislation.

Colorado Democrat Diana DeGette, a member of the House Energy and Commerce Committee, complained that Ms. Braly “could have said, ‘We’re going to investigate how to improve our risk pools,’ but she just said, ‘This is the way it is.'”

Illinois Democrat Jan Schakowsky, another committee member, said she felt Ms. Braly was lecturing the politicians: “It was like she was completely oblivious to the public reaction,” the congresswoman said.

This is exactly the kind of situation the 48-year-old Ms. Braly, a Texan with a friendly, low-key style, was brought in to handle. She beat out more seasoned competitors for the top job in 2007 because of the legal and public-policy chops she had honed in WellPoint’s general counsel’s office and later as its public-affairs and strategy chief.

In an emailed response to questions, Ms. Braly said she shared members’ concerns about premiums and didn’t want to raise rates.

During her grilling before the House subcommittee last week, Ms. Braly answered questions matter of factly and didn’t get flustered. And when Vermont Democrat Peter Welch asked her if she thought WellPoint’s premium increases were sustainable, she said, “Absolutely not.” Throughout the hearing she advocated requiring healthy people to buy insurance as a way to reduce premiums.

Ms. Braly declined to be interviewed for this story. But Brad Fluegel, the company’s chief of strategy, said that Ms. Braly knew about the rate increases in advance and decided they were necessary for the business. And Mr. Glasscock, Ms. Braly’s predecessor as CEO, defended the rate increases despite the political fallout. “I don’t think we anticipated this kind of response,” he said, “certainly not the magnitude of the response, but that’s hard to do.”

After initially being caught off guard by the severity of the reaction, aides said, it was Ms. Braly’s decision to come out swinging. While other executives discussed whether to lie low, Ms. Braly disagreed, said Mr. Fluegel. “Her response was, ‘OK, let’s get the facts out there,'” he said. “She views this as a teachable moment.”

Karen Ignagni, the lobbyist who leads the trade group America’s Health Insurance Plans, talked to Ms. Braly before the House hearing. She credits Ms. Braly’s public-policy background with the company’s decision to hold a briefing with the media ahead of the hearing to tell the insurer’s side of the story.

“WellPoint did something very important at that hearing by opening up and showing what’s going on,” Ms. Ignagni said. “That’s the first time we’ve seen those kinds of specifics.”

Still, behind the scenes the company is scrambling. On Monday, WellPoint planned a conference call with key insurance brokers to update them on the grilling its California leader, Leslie Margolin, got in the state legislature, and it canceled an investor meeting last month to do damage control related to the crisis.

And the company’s approach may not be playing so well with some of its allies. “I don’t think from a PR standpoint they’ve done a very good job,” said Philip Lee, who owns an insurance agency in Lafayette, Calif. “Maybe they need to take a more contrite and humble attitude and not come out fighting.”

Nevertheless, Mr. Lee said he continues to sell WellPoint plans because they are competitive with other carriers’ products. Relatively few of his clients would get the biggest, headline-grabbing rate boost, he said. Those who are likely to be hit by the pending increases have generally stuck with WellPoint, though they have often opted for reduced benefits.

About 800,000 people are expected to be affected by the rate adjustment in California.

Meanwhile, in Maine, where WellPoint is fighting a state regulator’s decision last year to reject part of its requested rate increase, its circle-the-wagons approach has drawn hostility from some officials. The company’s decision to seek another rate increase this year is “appalling,” said state Attorney General Janet Mills. “Everyone in Maine has tightened their belts.”

Last week, Colorado’s state insurance regulator, a Republican, announced an examination of the company’s recent rate increases, saying she was responding to a spike in consumer complaints. “We’re drilling down to the source to look at the numbers,” said Marcy Morrison, who is the state’s insurance commissioner.

In California, in addition to government scrutiny, WellPoint faces a plaintiff suit¿filed Monday in state court by the advocacy group Consumer Watchdog¿that alleges that when WellPoint raised rates as it was seeking to wind down certain health plans it didn’t provide mandated consumer protections, WellPoint said it hadn’t yet seen the suit.

Write to Avery Johnson at aver[email protected] and Anna Wilde Mathews at [email protected]