Rene Hernandez (second right) and his wife Nery Hernandez speak with Rosaly Hernandez, an insurance agent with Sunshine Life and Health Advisors, as they try to purchase health insurance under the Affordable Care Act at the kiosk setup at the Mall of Americas, Dec. 22, 2013, in Miami, Fla. (Joe Raedle/Getty Images)

A rush of last-minute health insurance shoppers visited HealthCare.gov Monday as the Centers for Medicare and Medicaid Services (CMS) announced on Twitter the site had "surpassed a million site visits."

Of course that doesn't mean that many people actually signed up for health insurance through that website, just that they visited the site on what was supposed to be the final day people could sign up if they wanted health insurance under the Affordable Care Act to kick in on Jan. 1.

T he White House announced Monday that the deadline would be extended through Tuesday.

Those who want insurance starting New Year's Day "should sign up today" but "if you have trouble due to high-demand, we will make sure we help you get signed up," said CMS spokeswoman Julie Bataille in a statement.

By 2 p.m. ET Monday there had about 850,000 visits to HealthCare.gov, approximately five times higher than last Monday, Bataille said, adding that the site had more than 1.2 million visits over the weekend.

The site has deployed a queuing system to accommodate the high traffic. That means if someone trying to buy insurance visited the site during a period of high traffic they may have been greeted by a page that tells them they can wait or to leave their e-mail address and they will be contacted to log back on when traffic is lighter. More than 60,000 potential consumers provided an e-mail address to get invited back later, officials said.

ABC News visited one of the locations today where consumers were trying to sign up in person. A group of between five to seven people waited at the Martin Luther King Jr. Memorial Library in downtown Washington, D.C., to try and sign up with health care navigators - people who assist in the process of signing up in person.

There were two women with two very different experiences.

Liz Meitner, 56, said she has been trying to sign up for health care since the very first day enrollment was available and has been stymied at every turn.

On Oct. 1, she said she had trouble with the District of Columbia's online health care exchange. She then waited five days before submitting a written application, another month went by and she was told she would have an answer two weeks later, but never getting that answer today she came to apply in person.

Meitner said she was told she had to wait while one of the health care navigators was on hold on the phone assistance line. When ABC News checked in with her by phone this evening, she said five hours later she was still in the library, still hoping to get an answer.

Meitner said she is unemployed and has a pre-existing condition so she said this is the only way for her to get health insurance. She said she feels "absolutely powerless."

"The idea is good, the implementation has been unsuccessful as far as I'm concerned so far," Meitner told ABC News. "I'm almost in shock. It's just hard to believe they could be so inefficient with something so important."

It was a very different experience for 25-year-old Desiree Hollar, who came to the library today and spent about 70 minutes waiting and meeting with a navigator before leaving. She was not able to finish her application either because she was told there was a computer server issue, but she was both upbeat and confident that after getting farther in the process than she had been able to online she would be able to submit an application before the deadline.

"I was screaming for a little bit," Hollar said, referring to her frustrations in trying to sign up either online or on the phone. "But ultimately it's fine to come down" to meet with navigators.

She said it was hard for her to figure out exactly where the navigator locations were, but said once she figured that part out "coming in person was great, it was so much easier and quicker."

Hollar said she would have come in sooner, but trying to find a location and getting time off work proved difficult. Hollar said she hopes to sign up for the cheaper "catastrophic" insurance because of her age and health instead of going with a more expensive plan.

Health industry analysts say at least 40 percent of the people that sign up need to be young and healthy or future premiums could skyrocket.

President Obama announced Friday that more than 1 million Americans selected health plans through the state and federal insurance exchanges to date under Obamacare.

ABC News' Devin Dwyer and Mary Bruce contributed to this report.