But the presentation showed that the administration had enjoyed much more success in obtaining public assistance records. Twenty-nine states and one California jurisdiction had signed agreements to disclose aid recipients under the Supplemental Nutrition Assistance Program, commonly known as food stamps.

The documents show that career professionals at the Census Bureau repeatedly warned that it would be difficult or impossible to compile a list of noncitizens from such records, especially in time to subtract them from the population totals used to reapportion the House, which were due on the last day of 2020.

The list of noncitizens was a priority for two political appointees whom Mr. Trump had placed in the bureau’s senior management, Nathaniel T. Cogley and Benjamin Overholt.

Census Bureau experts had been “consistently pessimistic” about their ability to find and remove undocumented residents from population totals used in apportioning the House, the agency’s top career official, Mr. Jarmin, wrote in an email to Mr. Cogley and the head of the Census Bureau, Steven Dillingham, shortly after Mr. Trump ordered the noncitizens list.

The pressure from the political appointees to come up with a number remained intense, as the September 2020 memorandum emailed to Mr. Jarmin; another top career official, Enrique Lamas; and the bureau’s chief of staff, Christa D. Jones, made clear.

The memo appears to have been a draft of talking points about political interference that officials wanted to raise with Mr. Ross before reapportionment figures were to be delivered to Mr. Trump. It began with an observation that the Commerce Department was “demonstrating an unusually high degree of engagement in technical matters” involving the calculation of population totals, a pattern of interference it called “unprecedented relative to the previous censuses.”

Point by point, the memo described political involvement in crucial aspects of the census.

One key process dealt with the bureau’s use of computer formulas to make educated guesses about who and how many people lived in households that had failed to complete census forms — calculations directly related to the totals used to apportion the House and draw new political maps. Another centered on a controversial new method known as differential privacy that the bureau sought to use to shield the identities of the people it counted.

Political appointees also had taken interest in how the bureau would produce final population figures needed to draw political maps nationwide, as well as estimates of the number of voting-age citizens. Mr. Trump had said he wanted to give those estimates to states as the basis for drawing political maps — another tactic that almost certainly would boost Republican political representation. The memo also said political officials had pushed to reduce the steps used to process and double-check population data so that apportionment figures could reach the White House on time.

The final complaint, about meddling in the methodology used to count undocumented immigrants, came to a head last January, when unnamed whistle-blowers accused Mr. Dillingham, Mr. Trump’s appointee to head the bureau, of caving to political pressure to produce a tally of noncitizens that experts said could not be assembled. Mr. Dillingham, who denied the charge, later resigned.

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