States would lose the waivers unless they find more people jobs, officials said.
The policy became a flash point in the election as Republicans accused Obama of "gutting" welfare's work requirement.
The House first voted to block the waivers in September, 250-164. Efforts to do the same in the Senate went nowhere.
On Wednesday, House Ways and Means Chairman Dave Camp (R-Mich.) said the federal Health department wants to weaken the work requirements, "pure and simple."
Officials have "attempted to hide their intentions by subsequent announcements saying they will only accept waiver proposals that result in greater numbers of welfare recipients working," Camp said.
"But nothing in current law prohibits a state from strengthening its work requirements and moving more individuals from welfare to work."
Democrats called the bill a political stunt that ignores calls by red and blue states for greater flexibility under TANF.
Opponents also noted that no states have applied for or been given waivers.
"This is a political solution in search of a problem," said Rep. Xavier BecerraXavier BecerraHispanics are split in DNC race Becerra launches 2018 bid for full term as California AG The green movement must continue in Trump era MORE (D-Calif.), chairman of the House Democratic caucus. "It handcuffs the ability of governors to have the flexibility they need to put people to work."
TANF is due for reauthorization at the end of the month.
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