(Photo Credit: Jon Elswick/AP Photo)

People who are unable to finish applying for health insurance by midnight may still be able to get coverage beginning Jan. 1 if they can show that they missed the Tuesday deadline because of problems with HealthCare.gov, the Obama administration said today.

Officials caution that the deadline remains today at midnight, but will consider individual circumstances that prevented consumers from finishing their application, judging those on a case-by-case basis.

This is just the latest extension of the sign-up period by the administration. The original deadline for people seeking coverage that begins Jan. 1 was Dec. 15. It was later extended to Dec. 23and then Monday the White House added another 24 hours through midnight today.

"We know many of you have been working hard to finish enrolling in a health plan in the Health Insurance Marketplace. Even though we have passed the December 23 enrollment deadline for coverage starting January 1, we don't want you to miss out if you've been trying to enroll," visitors to HealthCare.gov read Tuesday afternoon. "Sometimes despite your best efforts, you might have run into delays caused by heavy traffic to HealthCare.gov, maintenance periods, or other issues with our systems that prevented you from finishing the process on time. If this happened to you, don't worry - we still may be able to help you get covered as soon as January 1."

The site then directed visitors to the phone line, which is closed Christmas Day, and once a visitor explains how they have "been trying to enroll and explain why you wouldn't finish by deadline," a customer service representative will be able to tell the consumer "what you can do to finish your enrollment and still get covered for 2014."

The phone lines have also had long hold times. The federal health care website has had a surge of traffic in the past few days and this is basically a soft extension to provide for that increase, but will undoubtedly be another point of criticism for those opposed to the law.

Julie Bataille, spokeswoman for the Centers for Medicare and Medicaid Services (CMS), today said that Monday was a "record day" for the federal website and that the state exchanges and HealthCare.gov received 2 million site visits and the call center received more than 250,000 calls.

Bataille said volume "remained high, but not equal to yesterday."

"We have developed a robust casework process to address individual inquiries, respond to specific situations, and help consumers transition to new coverage," Bataille said in the same agency update.

The soft extension will not apply to anyone seeking insurance for the first time after midnight. If consumers sign up on HealthCare.Gov after midnight tonight, the earliest they can obtain insurance is Feb. 1, not Jan. 1.

In tweets posted by @HealthCare.Gov after the announcement, officials tried to clarify the new information, writing, "Like with Medicaid + Medicare, there's a casework system for ppl who tried to enroll but couldn't - considered on case by case basis."