Now the Obama administration is weighing in, asking state insurance regulators to take a closer look at rate requests before granting them. Under the Affordable Care Act, state agencies largely retain the right to regulate premiums in their states. So far only a handful have finalized premiums for the coming year, for which enrollment begins in November.

Still, wrote Counihan, "many issuers are reporting a decline in pent-up demand for services," which would lead to lower premiums. The letter also said that health care costs are not growing as fast as some had predicted, "even accounting for rapid growth in pharmaceutical costs."

Several recent studies bolster Counihan’s case.

An analysis of proposed rates by the consulting firm Avalere Health found that for a 50-year old non-smoker, premiums for the lowest-cost silver plan will rise by an average of 4.5 percent in the eight states they studied. Average premiums for the second-lowest silver plan will rise by only 1 percent. (Most analyses of premiums look at silver-level plans because they have been by far the most popular, attracting more than two-thirds of those who have signed up using the exchanges.)

A separate analysis by the Kaiser Family Foundation found similar results: increases should average about 4.4 percent for the two least expensive silver plans in the 10 major cities it studied. (Kaiser Health News is an editorially independent project of the Foundation.)

Both analyses, however, warn that consumers may only be able to avoid increases by changing insurers. "In these markets, consumers will need to balance continuity of care with lower monthly premiums when comparing their health insurance options," said Avalere Senior Vice President Caroline Pearson.

But insurance industry consultant and frequent Obamacare critic Robert Laszewski says that forcing people to change plans in order to avoid huge increases is just one problem of many.  "This is a debacle. This is a blow-up. This is a mess," he said. "There's big trouble in Obamacare land. The biggest carriers are losing their shirts" and thus seeking the biggest rate increases.

Why the disagreement? Mostly because there are outside factors pushing insurers to both raise and lower premiums.

For example, some insurers underestimated how many sick people would sign up, or how sick they would be. Last year was in some ways a huge social experiment. Insurers knew that the people who most needed insurance but had been previously shut out of the market would be the first to sign up for coverage. What they didn't know was how much health care they would consume. Those that guessed wrong and ended up spending more on care than they collected in premiums need an increase to make up the difference.