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Rep. William Lacy Clay, Missouri Democrat, held up a photo of the warehouse where millions of already printed census forms are stacked seven-stories high, waiting to be mailed out next year.

Mr. Baca, who mentioned Mr. Vitter’s association with an escort, has introduced a competing bill that would write into law that no question about citizenship or immigration status may be included in the decennial census.

Questions about citizenship have been included in other census questionnaires that go to smaller samples than the decennial census. The results suggest that California would have five or six fewer seats than it does now if only citizens were counted. Mr. Vitter said the states that lose out on seats under the current system are Iowa, Indiana, Mississippi, Oregon, Pennsylvania, Michigan, South Carolina and his own state of Louisiana.

Democrats have tried once to end the filibuster but were three votes shy of the 60 votes needed to overcome Republicans’ blockade, though three Democrats missed that vote.

For now, Mr. Vitter remains deadlocked with Democratic leaders. A spokeswoman for Sen. Barbara A. Mikulski, Maryland Democrat and chairman of the spending subcommittee that wrote the bill, could shed no light on when Democrats might try to break the impasse.

While he said changing apportionment is unconstitutional, Mr. McDonald said it was an open question whether individual states could use citizenship numbers to draw their congressional district lines.

He said Kansas and Hawaii have excluded nonresidents in drawing some district lines for their state legislatures. In the case of Hawaii, the location of a military base could have led at one point in the past to a state district with no eligible voters.