WASHINGTON — President Obama was seething. Two weeks after the disastrous launch of HealthCare.gov, Mr. Obama gathered his senior staff members in the Oval Office for what one aide recalled as an “unsparing” dressing-down.

The public accepts that technology sometimes fails, the president said, but he had personally trumpeted that HealthCare.gov would be ready on Oct. 1, and it wasn’t.

“If I had known,” Mr. Obama said, according to the aide, “we could have delayed the website.”

Mr. Obama’s anger, described by a White House that has repeatedly sought to show that the president was unaware of the extent of the website’s problems, has lit a fire under the West Wing staff. Senior aides are racing to make sure the website is fixed by the end of the month as they confront the political fallout from presidential promises, now broken, that all Americans who liked their existing health care plans could keep them.

Inside the White House, there is anxiety that if the health care problems are not righted, they could imperil the rest of Mr. Obama’s presidency, especially as criticism grows that the president misled consumers about the plan. Mr. Obama sought to tamp down that criticism by apologizing in an interview with NBC News on Thursday. “I am sorry that they, you know, are finding themselves in this situation, based on assurances they got from me,” the president said.