Another Census Bureau paper said "it is coincidental and unfortunate timing" that the survey was overhauled just before major provisions of the health care law took effect. "Ideally," it said, "the redesign would have had at least a few years to gather base line and trend data."
The old questionnaire asked consumers if they had various types of coverage at any time in the prior year. The new survey asks if they have insurance at the time of the interview — in February, March or April — then uses follow-up questions to find out when that coverage began and what months it was in effect. Using this technique, census officials believe they will be able to reconstruct the history of coverage month by month, over a period of about 15 months, for each person in a household.
Read MoreWhy we're investing in health care IT: BlackBerry CEO
However, Mr. O'Hara of the Census Bureau said the agency was not planning to release coverage data from early this year in its next report. Agency officials want to assess the reliability of the monthly data, being collected this year for the first time.
The White House is always looking for evidence to show the benefits of the health law, which is an issue in many of this year's midterm elections. The Department of Health and Human Services and the White House Council of Economic Advisers requested several of the new questions, and the White House Office of Management and Budget approved the new questionnaire. But the decision to make fundamental changes in the survey was driven by technical experts at the Census Bureau, and members of Congress have not focused on it or suggested political motives. The new survey was conceived, in part, to reduce a kind of bias or confusion in the old survey. When asked about their insurance arrangements in the prior year, people tended to give answers about their coverage at the time of the interview — forgetting, for example, if they had Medicaid for a few months early in the prior year.
People are continually moving on and off Medicaid rolls. The number of people who say in surveys that they have Medicaid coverage is almost always lower than the enrollment figures reported by federal and state agencies that administer the program.
The new survey asks people if they have coverage through an exchange, if it has premiums and if the premiums are subsidized.
People generally know if they have health insurance, but not necessarily the type of coverage. A study by the Census Bureau said that the line between public and private coverage is blurry.
Read MoreBeware of drinking Coca-Cola's Kool-Aid
"The same exact coverage will be construed as private by some and public by others," it said.
Census Bureau research in Massachusetts found that consumers "inevitably conflate Medicaid and the subsidized exchange." And many people with subsidized private insurance, purchased on the exchange, said they were receiving coverage from the government or the state.
Such perceptions are understandable. "Exchange coverage is a hybrid, partly private and partly government," said Joanne Pascale, a Census Bureau researcher who helped develop the new questionnaire.
The new survey also includes more detailed questions about whether people were offered insurance at work and whether they accepted it. If a worker is not in an employer's plan, the government asks why.
Kathleen Thiede Call, a professor at the University of Minnesota School of Public Health, said, "The health insurance data reported in September of this year will not be directly comparable to what was reported last September."
But Ms. Call, who was consulted by the Census Bureau, said: "I am excited about the redesign of the survey. For the first time, we will be able to look at monthly changes in coverage over a 14- or 15-month period, which was not possible with the old version of the survey."
—By Robert Pear, The New York Times