President Obama explained that the designers of Obamacare implemented an "insufficient" grandfather clause, the defects of which have led people to lose insurance policies that they like, contrary to his oft-repeated promise.

"There is no doubt that the way I put that forward unequivocally ended up not being accurate," Obama said of his pledge that if Americans have an insurance plan that they like, they could keep it under Obamacare. "It was not because of my intention not to deliver on that promise. We put a grandfather clause into the law, but it was insufficient."

He also said he was not warned of the website's technical problems. "I don't think I'm stupid enough to go around saying this is going to be like shopping on Amazon or Travelocity [if he'd known the site wouldn't work]," Obama told reporters.

Quinnipiac found Obama's credibility hit a new low this week. "For the first time today, American voters say 52 - 44 percent that Obama is not honest and trustworthy," the pollster said Tuesday. The survey came out as news of canceled policies dominated the headlines.

"My working assumption was that the majority of those folks would find better policies at lower costs or the same costs in the marketplaces, and that [for] the universe of folks who would not find better deals in the marketplace, the grandfather clause would work sufficiently for them," he said. "And it didn't."

The president denied that he gave a simplistic description of the effects of the law while trying to pass Obamacare in order to avoid the political difficulties that a more complex summary might invite.

"My expectation was that, for 98 percent of the American people, either it generally wouldn't change at all or they'd be pleasantly surprised with the options in the marketplace, and the grandfather clause would cover the rest," he said.