The Obama administration provided a few details Tuesday about a special enrollment period for Americans who sought to sign up through the online federal health insurance marketplace for coverage starting Jan. 1 but failed to obtain it.

In a blog post under the heading, "Couldn't enroll by December 23? We can still help you get covered," the Centers for Medicare and Medicaid explained that individuals could reach out to a network of federally-sponsored call centers around the country any day this week besides Christmas Day to try to complete their health insurance applications.

“If you weren’t able to enroll in an insurance plan by Dec. 23 because of problems you had using, you still may be able to get coverage that starts Jan. 1,” the post reads. “Even though we have passed the Dec. 23 enrollment deadline for coverage starting Jan. 1, we don’t want you to miss out if you’ve been trying to enroll."

“Sometimes despite your best efforts, you might have run into delays caused by heavy traffic to, maintenance periods, or other issues with our systems that prevented you from finishing the process on time," it continues. "If this happened to you, don’t worry — we still may be able to help you get covered as soon as Jan. 1.”

During the past two weeks, Health and Human Services Secretary Kathleen Sebelius and other senior administration official have reminded reporters that rules for the federal insurance exchange include a "special enrollment period" for those who tried but failed to meet the deadline for getting coverage starting on New Year's Day. But they had not spelled out until now how consumers could ask for the special consideration.

The official deadline was Dec. 23, but administration officials have given people an extra 24 hours -– until 11:59 p.m. on Christmas Eve -- to sign up by quietly changing the computer system's software over the weekend. There is no mention of the extension on the site. The difference between the extra 24 hours and the special enrollment period is that anyone who chooses a health plan by the end of Dec. 24 will automatically be assigned for coverage starting Jan. 1. Starting on Dec. 25, requests for Jan. 1 coverage  will be considered on a case by case basis.

The information about the special enrollment option came as CMS spokeswoman Julie Bataille issued a statement Tuesday  saying the federal online health insurance enrollment system received two million visitors Monday, while the government's call centers received more than 250,000 calls from Americans that same day.

The influx of visitors to meant more than 129,000 people entered the site's queuing system, Bataille said. Once in the queue, applicants were asked  to submit an e-mail so they could be alerted to when demand was less intense.

"All of them received e-mails inviting them back the same day to complete their applications," she said.

CMS continued to process applications for insurance Tuesday, Bataille added. "Volumes remain high but not equal to yesterday, and we have not had to deploy our queuing system," she said. "We are taking thousands of calls at our call centers, which remain open until midnight, and we are seeing thousands of visitors complete enrollment online."

Consumers who try and fail to enroll by midnight on Christmas Eve should contact a call center for "individual assistance," Bataille said, so that they can participate in "a robust casework process to address individual inquiries, respond to specific situations and help consumers transition to new coverage."

Amy Goldstein contributed to this report.