Rep. Roy Blunt, R-Mo., the House minority whip, and Sen. Mel Martinez, R-Fla., the Republican Party national chairman and a sponsor of the No Child Left Behind Act in 2001, were among the 57 who announced their decision Thursday, the Washington Post reported.
"The overwhelming intrusion of No Child Left Behind is too large to deal with unless you fundamentally change the legislation," Blunt said.
The legislation would allow states to opt out of the law's stringent testing requirements without risking federal aid.
Rep. George Miller, D-Calif., who heads the Education and Labor Committee, accused the Republicans of "trying to dismantle" the bill.
"Their irresponsible and unacceptable proposal would send billions of federal taxpayer dollars to the states with no accountability for how it is spent," he said.