“Insurers and the government have developed a symbiotic relationship, nurtured by tens of billions of dollars that flow from the federal Treasury to insurers each year,” said Michael F. Cannon, director of health policy studies at the libertarian Cato Institute.

So much so, in fact, that insurers may soon be on a collision course with the Republican majority in the new Congress. Insurers, often aligned with Republicans in the past, have built their business plans around the law and will strenuously resist Republican efforts to dismantle it. Since Mr. Obama signed the law, share prices for four of the major insurance companies — Aetna, Cigna, Humana and UnitedHealth — have more than doubled, while the Standard & Poor’s 500-stock index has increased about 70 percent.

“These companies all look at government programs as growth markets,” said Michael J. Tuffin, a former executive vice president of America’s Health Insurance Plans, the main lobby for the industry. “There will be nearly $2 trillion of subsidized coverage through insurance exchanges and Medicaid over the next 10 years. These are pragmatic companies. They will follow the customer.”

The relationship is expected only to deepen as the two sides grow more intertwined.

Consumers are already hearing the same messages from insurance companies and the government urging them to sign up for health plans during the three-month enrollment period. Federal law requires most Americans to have coverage, insurers provide it, and the government subsidizes it.

“We are in this together,” Kevin J. Counihan, the chief executive of the federal insurance marketplace, told insurers at a recent conference in Washington. “You have been our partners,” and for that, he said, “we are very grateful.”