Those sources likely include Census Bureau and Centers for Disease Control and Prevention data, which are collected every year. Garfield said much of the data likely won't be available until winter 2015.
In the meantime, public and private entities are conducting their own surveys to get an idea of who's signing up. Garfield said this is a valid way of getting reliable numbers, but it's challenging because most of the general population is not experiencing changes in coverage through the law right now.
Of course, only the government and insurance companies have access to lists of people who have signed up and are the only ones able to limit a survey to that group.
(Read more: Doing the Obamacare math for women)
About 5 million people overall had enrolled in ACA plans as of March 17, according to the Centers for Medicare and Medicaid Services (CMS).
Critics have suggested most of them had insurance before, but had to buy new plans because their old ones were not compliant with the new law.
The Obama administration has touted a recent Gallup poll that found the rate of uninsured Americans dropping to 15.2 percent in February—the lowest rate since 2008.
But McKinsey, a leading management consulting firm, polled about 2,100 exchange-eligible Americans in February, and found only 27 percent of people who had picked a plan were previously uninsured. Only 53 percent of them had paid their first premium, compared with 86 percent of the previously insured. With 5 million total enrollments, that would be about 715,500 previously uninsured Americans who had chosen and paid for new insurance.
It's also been hard to get a handle on how many previously uninsured people have gained coverage through Medicaid expansion in the states that chose to offer it.
The House Energy and Commerce Committee has held numerous hearings on the Obamacare implementation. Chairman Fred Upton has been a vocal critic.
"It's bad enough that the administration has repeatedly moved the goalposts and attempted to redefine what success means for the president's health care law. But the fact that they are deliberately avoiding the threshold measurement of how many of the law's new enrollees were previously uninsured begs the question: what was the goal?" the Michigan Republican said in a statement to CNBC.
—By CNBC's Jodi Gralnick. Follow her on Twitter @jodigralnick.