Last month, the news site ProPublica reported that nearly 1 million transactions had occurred on HealthCare.gov since the close of open enrollment.
ProPublica's report, which was based on a Freedom of Information Act document request to HHS, noted that a transaction could include not only new enrollments, but also changes in plans by people who had a so-called qualifying life event. Still, the volume of transactions suggests there could be a significant increase in the total number of sign-ups.
Gaba argued that HHS should be releasing official numbers during the special enrollment period for several reasons.
"For one thing ... the numbers are still going up," he said. Gaba added that Obamacare is such a big issue that the public deserves to know how the program is doing, without having to wait until open enrollment begins.
Read MoreSubsidy, what subsidy? Obamacare's clueless
"The Democrats lost the House of Representatives over this ... it has certainly sucked the oxygen out of Washington for the better part of the past four years," Gaba said. "It's important to give updates on a fairly regular basis."
He noted that the exchange run by the state of Minnesota "is almost doing daily updates. It's like an odometer."
And Oregon's exchange updates its enrollment weekly.
"I wouldn't think it would be terribly difficult" for HealthCare.gov to give such regular updates, said Gaba, noting HHS' monthly Medicaid enrollment reports.
Gaba's estimates of the current enrollments reflect only sign-ups—not possible drop-offs. He acknowledged that even as a number of people sign up, some people—possibly more—will drop their plans because they can't afford them or for other reasons. But if HHS doesn't reveal its tally, then it allows Obamacare opponents to argue that the administration has something to hide.
"If you don't release the data, then the sky's the limit—they can say anything they want," he said.
Kevin Counihan, the head of Connecticut's state-run Obamacare exchange, said he's made it a practice to release what data he can about enrollment, as well as any problems the exchange had in its operation "to create and maintain credibility."
"I may be wrong in this, but when you've got something this new and this ideologically polarizing, the best way to try to get support from both sides is to share information," Counihan said. "If you create trust, you create a buffer when things go bad."
—By CNBC's Dan Mangan