The GOP cited data showing welfare caseloads have decreased by 57 percent since TANF was enacted.
The administration's announcement will "undo policies that have led to more work and earnings and less welfare dependence and poverty among low-income Americans," the memo read.
The committee's chairman, Rep. Dave Camp (R-Mich.), called the new policy a "brazen and unwarranted unraveling of welfare reform" after it was first announced on July 12. "This ends welfare reform as we know it," he said.
But the leading Democrat on Ways and Means, Rep. Sandy Levin (D-Mich.), argued that Republicans' stance is hypocritical.
"This policy is pro-work, and it acknowledges that not all wisdom resides in Washington," he said in a statement. "Curiously, some of the same voices that pay lip service to the virtues of state flexibility now appear to oppose providing waivers under the TANF program. It turns out that Republican support for state flexibility is a one-way street."