The court said without comment Monday that it will not step into a lawsuit that questioned whether public schools have to comply with requirements of the law if the federal government doesn't pay for them.
A federal judge dismissed the lawsuit and a federal appeals court split 8-8, leaving the judge's ruling in place.
The No Child Left Behind Act became law in 2002. It requires tests on subjects including math and reading in grades three through eight, and once in high school. Schools that miss testing benchmarks face increasingly stiff sanctions, including the potential loss of federal money.
President Barack Obama is proposing major changes to the law. Obama already has markedly increased federal money for public schools.
The case is School District of Pontiac, Mich. v. Duncan, 09-852.