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Sen. Tom Coburn, Oklahoma Republican, said he received an American Community Survey last year and filled out only half of the questions.

“There’s nothing in the Constitution, in the first article, that gives the power of the census to do that,” he said, adding that he would “defend anybody” who doesn’t want to complete the long-form questionnaire.

Mr. Groves said he accepts the criticism that his bureau has not publicized the American Community Survey well enough but that fewer responses raise government costs because workers have to visit the homes to try to track down the answers.

The law says there is a penalty for not filling out the American Community Survey, but Mr. Groves said he knows of no prosecutions.