Dennis Willingham knew when he took the job as superintendent in Walker County, Ala., that money for schools would always be tight.

That is the nature of public education in a rural area with few wealthy residents to tax and a student body that is nearly 70 percent lower income.

But since the White House temporarily withheld federal dollars from schools this summer and proposed cutting federal education spending next year, Dr. Willingham has felt a new pressure.

Walking around schools in his district, a mostly white, Republican area northwest of Birmingham with 6,700 students in the county schools, Dr. Willingham sees federal dollars everywhere. In the after-school program and the robotics club, in the high school students taking classes for college credit.

“The federal dollars are our lifeline,” Dr. Willingham said.

President Trump has targeted federal funding for education in his second term, embracing a longstanding conservative argument that the federal government adds bureaucracy without meaningfully improving student achievement. He has pledged to “return” education to states, which already have primary oversight over schools.