Next year’s head count already faces daunting challenges. A wave of immigration not seen since the early 1900s has brought into the country people who are either unaware of the importance of the American census or are suspicious of those that were conducted in their native countries. The 2020 count already has been tarred by a ferocious battle over Republican efforts to enumerate noncitizens nationwide, a fight that is likely to depress census response next year among minorities who are mistrustful of the government. The Census Bureau works to encourage participation, but this time around, its resources are spread especially thin.

Local leaders regard the tally as a once-in-a-decade chance to top up federal subsidies for crucial services like education and health care that are based on population. “We have this one shot,” said Erika Reyna-Velazquez, the assistant chief of staff to the Hidalgo County judge in Edinburg, Texas, in the Rio Grande Valley near the border with Mexico. “And if we miss it, we’re going to be undercounted again for the next 10 years.”

In Texas, a bill to commit $50 million to census response died this spring in the Republican-controlled Legislature. Representative César J. Blanco, the El Paso Democrat who sponsored the bill, claimed that the Legislature wanted to blunt a demographic shift that has strengthened Democrats. “They’re concerned that if you have a more accurate count, it would put them at a disadvantage,” he said.

That comes at a price, said Daniel A. Smith, a professor of political science at the University of Florida. “To send a political statement that you don’t want people to be counted, which might reduce the amount of federal funding your state gets, would seem to be cutting off your nose to spite your face,” he said.

Texans could need that money. The state adds more than a thousand new residents daily. Half are newborns. Nearly 30 percent hail from foreign countries, a hefty share from Asia.

The remaining 20 percent moved from other states, led by California, which is expected to lose a House seat for the first time ever — and which is sparing no expense to maximize its census tally. Although the Census Bureau publishes a map showing the predicted likelihood of a low response rate in most of the nation’s 73,057 census tracts, California commissioned its own map, ranking a tract’s expected census response according to 14 variables like education, income and housing type (a tract in Stockton, in the Central Valley breadbasket, is the toughest target).