The White House has decided to allow an extra 24 hours for people to sign up for insurance on HealthCare.gov, through the end of the day Tuesday, to receive coverage beginning on Jan. 1, according to a senior official familiar with the change.

The official deadline for getting insurance remains 11:59 p.m. on Monday. But because of record traffic on the website Monday morning, officials wanted to reassure the public — and themselves — that people who sought coverage in good faith would be covered. The extension was first reported by The Washington Post.

The official said the administration does not want to encourage people to wait until Tuesday to come to the website, because it fears more record numbers.

“We recognize that many have chosen to make their final decisions on today’s deadline, and we are committed to making sure they can do so,” said Julie Bataille, a spokeswoman for the Centers for Medicare and Medicaid Services. “Anticipating high demand and the fact that consumers may be enrolling from multiple time zones, we have taken steps to make sure that those who select a plan through tomorrow will get coverage for Jan. 1.”

An administration official said the extension would allow officials to “handle heavy online traffic or other technical issues.” The website has been plagued by technical problems since it was launched on Oct. 1.

A queuing system, or waiting room, kicked in early Monday to handle what officials said was the highest volume of traffic the site has seen since it opened. That should keep the site from crashing by asking people to return at a time when the site is less crowded.

But officials said they wanted to accommodate everyone who wanted to get insurance, much as polling places try to stay open later on election night to accommodate those who are already in line to vote when the polls officially close.

People calling the federal exchange on Monday morning were greeted with a recorded message that said: “Welcome to the health insurance marketplace. We are currently experiencing longer-than-normal hold time. Do you need coverage for Jan. 1? Please stay on the line, as your call is important to us.”

The government told callers to be prepared for a long wait. “If you are using a cell or cordless phone, make sure it’s fully charged,” the message said.

Over the weekend, President Obama, who is on vacation in Hawaii, took advantage of his own signature legislative achievement and enrolled in a health care plan offered through the District of Columbia marketplace.

Though the act is entirely symbolic — the president and his family receive health insurance through the military, and will continue to do so after they leave the White House — the administration hopes that Mr. Obama will set an example for many of the uninsured it is urging to sign up before the deadline.

Even though Mr. Obama will not actually use his new plan, a White House official said, “he was pleased to participate in a plan as a show of support for these marketplaces, which are providing quality, affordable health care options to more than a million people.”

The president opted for a bronze plan.

The enrollment period for people seeking individual insurance continues through March 31. To be sure of coverage in January, people were supposed to pick plans by Monday and pay the first month’s premium by Dec. 31.

The White House has encouraged insurers to relax those deadlines and provide coverage retroactive to Jan. 1 for people who sign up or pay later in the month. America’s Health Insurance Plans, the industry’s largest trade group, said its members would give consumers more time, to Jan. 10, to pay the first month’s premium.