After sidestepping the issue for weeks, President Obama on Thursday apologized to Americans who are losing their health insurance despite his repeated and emphatic promises that it wouldn’t happen.

The president made the admission on a day when Senate Republicans demanded that he fire his top health official in response to “undeniable” problems with Obamacare’s rollout and his White House fends off doubts that it can fix a balky website that is spoiling the health care law’s debut.

“I am sorry that they are finding themselves in this situation based on assurances they got from me,” the president told NBC in an interview recorded at the White House on Thursday afternoon. “We’ve got to work hard to make sure that they know we hear them and we’re going to do everything we can to deal with folks who find themselves in a tough position as a consequence of this.”

Mr. Obama’s comments represent something of an about-face for the administration, which until now had argued that Americans were aware all along — or should have been aware — that Obamacare would result in many people losing policies because they don’t comply with the law’s standards.