On April 4, a terse letter signed by the heads of the major education lobbying organizations in Washington — teachers unions, school boards, superintendents, principals and governors — landed on the desk of John King Jr., the secretary of education.

It had been less than three weeks since the Senate had confirmed Mr. King, a former high school teacher and education commissioner in New York. Yet as the letter showed, he had already managed to irk the entire school establishment, as well as the Republican majority in Congress. His offense? Trying to make good on a long-unkept promise to the nation’s low-income schoolchildren that they should receive as much education funding as everyone else.

A few months before this clash, Congress had finished renewing the omnibus federal education law known as the Elementary and Secondary Education Act (ESEA), after years of difficult negotiation. The next move was for the Education Department to issue regulations detailing how provisions of the law were to be put in place. The department proposed a rule that would require local school districts to give schools enrolling large numbers of poor children at least as much state and local money as other schools — thus prompting the letter.

Equal funding doesn’t sound too crazy, yet many districts currently fall short. Nationwide, districts with high levels of poverty receive $1,200 less per pupil from state and local sources than districts with low levels of poverty.

Marguerite Roza, a Georgetown University scholar, has found that many districts spend up to a third less per pupil in poor schools compared with others. This can happen for various reasons: because wealthy parents unduly influence budget allocations, for example. It can also happen because most teachers are paid using collectively bargained salary schedules that reward longevity. Senior teachers tend to cluster in wealthy schools, while schools where many children are poor often churn through large numbers of novice, badly paid teachers.

But fixing such funding inequities can be expensive, as well as disruptive to longstanding arrangements of which teachers get to be in which schools. That’s why the unions, districts and state leaders wrote the letter urging Mr. King to “refrain from defining terms and aspects of the new law” — the essence of regulation — “especially as it relates to the ‘supplement, not supplant’ provision.”

“Supplement, not supplant” is a key element of the education act, going back to the earliest version of the law, enacted five decades ago as part of President Lyndon Johnson’s war on poverty, and the roots of controversy stretch back that far as well.