The first big wave of new rules under the federal health care law goes into effect on Thursday, leaving many insurers scrambling to get ahead of the changes. Insurers are cutting administrative staff to lower overhead costs, investing in major technology upgrades and training employees to field the expected influx of customer inquiries.

Despite the talk among some Republicans of repealing all or part of the law, insurers say they cannot afford to put off the changes. Many said they are fundamentally altering their business models to cope.

“It is really the Manhattan Project because of the scale and the scope,” said Karen Ignagni, the chief executive of America’s Health Insurance Plans, a trade group.

Under the new law, insurers that offer child-only policies must begin covering all children, even the seriously ill, beginning Thursday. Insurers must also begin offering free preventive services, and for the first time, their premiums must start passing muster with both federal and state regulators by the end of the year.

Companies are choosing to avoid some of the new rules by no longer offering certain policies. Aetna, WellPoint and Cigna, for example, have announced that they would stop selling new child-only policies, at least in some states. Ahead of the regulatory review, some already raised premiums earlier in the year.

The coming weeks and months are seen as an important test of the legislation — and a dry run of sorts for the more far-reaching changes required by the law in 2014, when insurers will have to offer coverage to everyone and begin selling their plans on state-run exchanges.

Adjusting to the new terrain could push some insurers out of business, health care analysts said. In a setback to the bottom line, for example, insurers will no longer be able to pick and choose enrollees to avoid covering people who are likely to run up high medical bills, and many of the markets where they operate will become much less profitable.

“A lot of health plans will struggle and fail,” said Jeff Fusile, a health care partner at PricewaterhouseCoopers.

Blue Shield of California, which was an early proponent of requiring insurers to cover everyone, has trained about 2,500 people — about half of its work force — on the impact of the new law. About 250 of the employees are leading teams responsible for reprogramming computer systems, determining the cost of new policies and making sure the people answering the phone have answers to customer questions, among other tasks.

“The train has left the station, and we’d much rather be the ones with the engineer’s hat,” said Bruce Bodaken, the chief executive of Blue Shield, a nonprofit health plan based in San Francisco.

The challenge for the industry as a whole will be to demonstrate an ability to oversee patient care and work closely with hospitals and doctors to find ways to improve the quality of care — all the while making it less costly. To that end, insurers are making significant investments in technology systems and new areas of expertise.

Blue Shield says it has already increased its efforts to address the cost and quality of care by exploring new ways to pay doctors and hospitals. “We’re going to do a lot more innovation and experimentation, failing and succeeding, than we’ve ever being doing before,” Mr. Bodaken said.

Like many of its competitors, Blue Shield is also upgrading its technology systems. The plan is spending several hundred million dollars on the effort, and both the new and old systems must be reprogrammed at the same time to reflect the new rules.

But the cost of such upgrades could be the undoing of some plans, said Mr. Fusile, the health care partner.

“The biggest challenge facing the payers is that they are going through a pretty massive investment in information technology,” he said. “They have their plate pretty full from that.”

Even those insurers that were critical of the legislation have little choice but to comply. Still, several plans have chosen to avoid the new rules by ceasing to offer certain policies. In the case of the child-only policies, the insurers say the new rules could force them to cover too many sick children and too few healthy ones.