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One industry analyst has estimated that as many as 7 million people will have their policies canceled, requiring them to shop for plans under Obamacare that are often more expensive, especially if the consumer doesn’t qualify for a taxpayer-funded subsidy.

An insurance industry specialist, Larry Levitt of the Kaiser Family Foundation, said insurance companies have no choice but to take these actions. “It is administratively easier to cancel than change plans,” he said on his Twitter account.

As the furor grew Tuesday over canceled policies, the White House and its Democratic allies increasingly were casting blame on the insurance industry instead of the law.

Democrats raised a trial balloon for this offensive late Monday night from two key presidential aides.

Valerie Jarrett, one of President Obama’s most trusted advisers, wrote on her Twitter account: “Nothing in #Obamacare forces people out of their health plans. No change is required unless insurance companies change existing plans.” Deputy press secretary Eric Schultz published a near-identical tweet: “Don’t be fooled. Nothing in the ACA forces people out of their plans. No change is required unless ins companies change their existing plan”

The comments prompted a furious reaction, including from one conservative blogger who likened Ms. Jarrett’s explanation to saying “there’s nothing about land mines that forces explosions.”

The Democratic pushback coincided with a flurry of Capitol Hill activity on the botched Obamacare rollout.

At a House Ways and Means Committee hearing, the head of the agency overseeing the law apologized Tuesday to people who have tried to use the flawed federal website.

The House investigative panel issued a subpoena against Quality Software Services Inc. demanding documents that will show whether the contractor hired to build the federal Obamacare website took precautions on data security.

The White House tried to emphasize Tuesday that 80 percent of Americans will keep their insurance coverage, and “only” 5 percent of consumers will be required to purchase policies by March 31 — about 14 million people. Mr. Carney characterized the current insurance market as “the Wild West,” saying it has been “underregulated.”

As a result, he said, unscrupulous insurance companies have been free to leave consumers unprotected in a health care crisis.

“They could throw you off. They could jack up your premiums. They could change your coverage,” Mr. Carney said, ironically citing the same complaints of people whose policies are being canceled as a result of Obamacare.

When a reporter confronted Mr. Carney with the fact that many consumers are being forced out of plans they like, the president’s spokesman replied, “If you want to make that point, you can.”