Updated

Not even the nation's official head-counter will be able to keep track of the comprehensive impact of ObamaCare, critics warn.

The Census Bureau is in the midst of significantly changing its survey questions on health care, which some fear will make it difficult to give an accurate reading of how many people have gained insurance under the law.

The change was first reported by The New York Times. Republicans are now accusing the administration of overhauling the survey in order to obscure the effects of the Affordable Care Act.

"If the administration truly wants to know how many people have insurance today because of the health law, it will swiftly reverse course," House Energy and Commerce Committee Chairman Fred Upton, R-Mich., said in a statement. "Did the health law work to insure the uninsured? A simple check of a box could answer that question. Sadly, we may never know -- and the administration seems just fine with that."

ObamaCare enrollment ended for virtually everyone on Tuesday. The administration has touted that 7.5 million people signed up on the private exchanges, and more through Medicaid, since October.

But that number may be misleading. The administration still has not said how many people have paid their first month's premium and, perhaps more importantly, how many people had simply signed up on the exchanges after being kicked off their old plans. The administration has not been able to provide a number showing the net increase in insurance coverage.

Enter the Census Bureau. It was seen as a relatively reliable way to track the presumed increase in coverage. But changes in the survey questions have raised concerns that the bureau cannot offer an apples-to-apples comparison.

Asked about the changes, administration officials stressed to Fox News that they could at least gather one year-to-year comparison that is consistent. The new questions will cover the 2013 year, an official said, so "there will be a full year of data to compare to the year ACA takes effect."

Further, officials said the changes were years in the making, and that they were tested in 2010 and 2013 and found to work better.

"The recent changes to the Current Population Survey's questions related to health insurance coverage is the culmination of 14 years of research and two national tests in 2010 and 2013 clearly showing the revised questions provide more precise measures of health insurance through improved respondent recall," Census Bureau Director John Thompson said in a statement.

The Census Bureau has been at the center of political accusations since the very start of the Obama administration. Back in 2009, the administration decided to make the Census Bureau director work with the White House -- and not just the Commerce secretary -- leading to charges that the new Obama White House was trying to exert control over the ostensibly nonpartisan agency.

The latest report revived those claims.

"How convenient," Brendan Buck, spokesman for House Speaker John Boehner, tweeted in reference to the Times report.

Rory Cooper, spokesman for House GOP Leader Eric Cantor, tweeted that the administration is "now changing the CENSUS survey in order to hide failure of Obamacare."

Nothing of the sort, officials suggest.

Thompson said the change was announced in September and "implemented because the evidence showed that re-engineering the questions provides demonstrably more accurate results. The Census Bureau only implements changes in survey methodology based on research, testing and evidence presented for peer review."

The Times reported that the changes were spearheaded by technical experts at the bureau.

One internal document reportedly said it was just "coincidental and unfortunate timing" that the changes were going live around the time of the ObamaCare implementation.

According to the Times, the old questions asked people if they had coverage at any point in the prior year. The new questions ask if they have insurance "at the time of the interview," which in this case took place in February, March and April. Officials use that and other data to try to determine coverage over the last 15 months.

This is considered more accurate, according to the Times, because people often forget whether they had coverage in the past year when asked only that question.

Census officials said that the new method will let survey takers then work "backwards through time about specific months of coverage."

Fox News' Jim Angle contributed to this report.