Under the Affordable Care Act, nearly all Americans must have some form of health coverage for 2017 or face a potential tax penalty that is the higher of $695 per adult, or 2.5 percent of household income.
Tuesday's enrollment deadline is for sign-ups in individual health plans effective this year. After the deadline expires, most people will be barred from enrolling in individual plans, until 2018 enrollment starts next fall, unless they qualify for a waiver.
Lori Lodes, a former director of CMS' communication office, on Tuesday had tweeted that an extension should be granted.
"Whenever there was any sort of issue that prevented people from being able to sign up for health care ... whenever we had an issue that made that process difficult, or consumers weren't able to quickly sign up, we ended up doing an extension," Lodes told CNBC.
"You have to make sure that the site is working to give people reasonable access to sign up, and if they cannot meet that bar, then they need to extend the deadline," Lodes said of the Trump administration.
Lodes' former boss, ex-acting CMS Administrator Andy Slavitt, in an email to CNBC said, "On the day when record numbers of young people sign up, it's a great sign that people want coverage and are queued up."
"It would be good for consumers and smart for the risk pool for the administration to extend the deadline to ensure that all those people get the coverage they're seeking," Slavitt wrote. Young adults are more prone than other customers to wait until the final day of enrollment to sign up.
A risk pool is the pool of insurance customers whose costs from sicker customers are, ideally at least, more than offset by the premiums paid by healthier customers who use fewer medical services. Too many sick customers can lead to losses for insurers, and rising premiums for everyone.
Young adults are much desired by Obamacare insurers because they can lower the financial risk of selling Obamacare plans. But enrollment among that demographic has to day fallen fall short of insurers' hopes.
The head of a leading Obamacare advocacy group, Enroll America, issued a statement Tuesday calling on "the Department of Health and Human Services to allow every consumer who is in the online waiting room or placed in a queue on the telephone hotline before the deadline to complete the enrollment process."
"Despite the political uncertainty around the Affordable Care Act, we've continued to see very strong interest from consumers who want to find quality, affordable health insurance for their families," said Enroll America President Anne Filipic.
"We're gratified to see that strong demand continue into the final day of open enrollment."
Last week, the Trump administration said it was killing ads and other outreach efforts to promote HealthCare.gov.
But the administration soon partially reversed course, and allowed email reminders and tweets to go out to would-be HealthCare.gov customers to encourage enrollment.
As of earlier this month, more than 8.8 million people had signed up for coverage on HealthCare.gov. At least another 2.8 million had signed up in a plan sold on the other Obamacare exchanges, which are run by individual states and the District of Columbia.
Most customers of the government-run exchanges qualify for tax credits that lower the cost of their monthly plan premiums. Those subsidies are available to people with low and moderate incomes.