Even as President Barack Obama prepares to make a fresh push for his troubled healthcare program Tuesday, questions still remain about the error rates being seen HealthCare.gov.
The federal agency running the site on Monday repeatedly refused to reveal how many Obamacare enrollments to date have software-related errors that could delay enrollees' insurance coverage, even as it announced a major fix of those problems going forward.
The Centers for Medicaid and Medicare Services also refused to say when it had learned that up to 80 percent of the software errors affecting enrollment data were due to a single "bug" related to enrollees' Social Security numbers, and why it was disclosing that fact only Monday when it announced that bug has been fixed.
The bug may have affected an unknown number of the more than 125,000 enrollments that a source told CNBC have enrolled in coverage through HealthCare.gov since Oct. 1.
Despite these ongoing issues, the White House said Saturday that the website is working at an acceptable level. Obama is expected to discuss the healthcare program, formally known as the Affordable Care Act, at 2:30 p.m. Tuesday.
"In his remarks, the President will discuss the ongoing work to strengthen the website and reach Americans seeking these new healthcare options," a White House official told Reuters. "He will also focus attention back on the core principles of reform that have been lost in the attention on the website, and invoke the successes that are already flowing from the law."
However, it may be tough to shift the focus away from the website. An insurance industry source told CNBC.com that insurance plans are still having serious problems with 834 files.
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Questions about the so-called 834-error rate were already pressing before CMS' afternoon conference call with reporters about the status of HealthCare.gov, the federal government's marketplace for selling health insurance in 36 states. The number 834 refers to the type of file insurers use to enroll people.
The insurance industry source said the HealthCare.gov repair team has repeatedly put in supposed fixes that seem to solve problems on the website side but don't all resolve the problem on the insurers' side.
Asked about the 834 issue, White House spokesman Jay Carney on Monday said it is "a high priority" to make sure that people who have enrolled through HealthCare.gov "are aware of the steps they need to take" to call the website's call center or their insurer to make sure their enrollment has been processed correctly if they are not sure it has been.
(Watch: HealthCare.gov repairs take effect)
Since its Oct. 1 launch, HealthCare.gov has been plagued not only by lower-than-projected enrollments, but also by software glitches that have corrupted data in the enrollments sent to insurers for processing. Those problems are forcing insurers to painstakingly go over many of the enrollments they get from HealthCare.gov, often by hand, to correct the errors and then formally enroll people in coverage.
CMS in the weeks after the Oct. 1 launch downplayed suggestions that 834 errors were a significant problem, even after CNBC revealed that some insurers were seeing error rates of up to a staggering 99 percent of enrollments they were receiving. But in late October, Jeff Zients, the management expert brought in by President Barack Obama to oversee the repair effort of HealthCare.gov, told reporters the 834 errors were "at the top" of his list of fixes to make.
On Sunday, CMS had announced that a nearly two-month-long effort to fix the glitch-ridden website had led to HealthCare.gov working smoothly for most users by that day, and said the site would be able to handle up to 800,000 visitors per day. The repair effort was racing against a Dec. 23 deadline by which people must sign up for insurance coverage through the site to have coverage kick in by Jan. 1.
In the first 12 hours of operation Monday, HealthCare.gov had 375,000 visitors, which was about twice the volume of a typical Monday, said CMS spokeswoman Julie Bataille. She said a new queuing system to manage that traffic load was put into use for the first time to deal with the volume.
Hours later theHealthCare.gov Twitter feed announced that it had "750K visitors as of 5:30 pm, no queuing now, site fast w/low error rates."
Bataille also revealed that HealthCare.gov had launched "an improved window-shopping feature for consumers" allowing them to see plan premium prices, deductible and other copay amounts, and plan network details without having to fill out a time-consuming application.
Bataille then told reporters that the repair team working on the site had determined that "more than 80 percent of 834 production errors resulted from one bug that didn't allow a Social Security number to be entered" on the online enrollment file.
"That bug has been fixed and is now working properly," Bataille said, adding that CMS was "committed to getting accurate information" to insurers so that people could make sure their enrollments via HealthCare.gov had been processed.
Bataille then was peppered with questions from reporters about what the rate of 834 errors has been since HealthCare.gov launched. She repeatedly said she did not know the error rate, even after reporters pointed out that "80 percent" of 834 errors by definition had to be based on a number of errors.
"I will go back an see if there is an actual number," said Bataille, who has been asked often about the 834 error rate in conference calls with the media for more than a week.
(Read more: White House says don't rush to website)
Robert Zirkelbach, a spokesman for America's Health Insurance Plans, said, "Health plans continue to experience significant problems with the '834' enrollment files."
Carney, the White House spokesman, said: "We are very mindful of making sure that consumers who want coverage starting in January are able to get it. And CMS is reaching out directly to consumers who have already selected a plan to let them know to be in touch with their plan, to pay their first premium, to ensure that coverage is—kicks in and know that plans are working hard to make sure their new customers are covered as well."
"CMS is having daily conversations with issuers to get feedback from them," Carney said. "We have instituted a number of significant fixes to the so-called 834 forms. ... And we believe that the majority of fixes to 834 forms have been made, including significant ones that were made over the weekend. We expect the info now sent to insurers to be vastly improved. But we're going to continue to work with issuers to make sure that whatever remaining problems exist are addressed and fixed."
Bataille would not confirm what a source told CNBC earlier in the day, that about 100,000 people signed up for Obamacare insurance through HealthCare.gov in November.
She said officials were still checking enrollment data to make sure that it was accurate, and expected to release enrollment numbers in mid-December.
By adding October's enrollment numbers via HealthCare.gov, and more than 200,000 enrollments from the state-run health exchanges, a total of about 332,000 nationwide have enrolled in Obamacare so far.
—By CNBC's Dan Mangan and Bertha Coombs; Reuters contributed to this report.