Herbert's office declined to comment on the escalating political fight, only noting the state wants to avoid reporting rules it considers onerous.
The Department of Health and Human Services (HHS)has given states that chance, issuing a memorandum in mid-July that encouraged them to apply for a waiver as long as their plan would result in more people finding work.
Congressional Republicans, led by Sen. Orrin Hatch, R-Utah, immediately pounced on that memo, saying the administration has no authority to offer waivers to the landmark 1996 welfare law without an act of Congress and warned if allowed to stand it could result in states counting such things as "bed rest or smoking cessation" as work.
Hatch even introduced legislation that would block the program.
At the time, Democrats argued Hatch and Herbert were at odds with each other, a claim both have refuted.
Herbert sent HHS Secretary Kathleen Sebelius a letter on July 16 saying Utah didn't think the department had authority to issue waivers and would offer only a conditional endorsement of the plan.
"Utah would only support waiver authority where work and self-sufficiency were the basis of the program," Herbert wrote.
Hatch's staff said the senator, who is the top Republican on the committee overseeing welfare, believes flexibility is a worthy goal but only through a congressional reworking on the welfare law.
That 1996 law ended national welfare, replacing it with a state program funded through federal grants that provides assistance to the poor for a limited time and requires participants to get a job.
Romney touts himself as a big supporter of that law and noted Obama has said he wouldn't have voted for it, a dig that was part of a broad offensive on the issue launched Tuesday.
The Romney camp produced a 30-second ad accusing Obama of gutting welfare rules, intimating they would let people remain on government support indefinitely, and the GOP candidate beat the same drum during a speech in Illinois.
"If I'm president I will put work back in welfare," Romney said.
The campaign also released a barrage of statements from top Republicans hitting Obama on welfare, including one from Hatch.
"In another Washington power grab, President Obama has opted to gut the work requirements at the core of the bipartisan welfare reform passed in the 1990s," Hatch said. "This is an insult to the American people."
Carney called Romney's attack "categorically false" and an "utter misrepresentation of this president's policy."
He said the administration would reject any waiver proposals unless the states find a way to boost the number of welfare recipients who get jobs by 20 percent. And he noted that when Romney was the governor of Massachusetts, he signed a letter that asked for flexibility in the welfare rules.
"Hypocrisy knows no bounds," Carney said. "Perhaps his argument is with his past self."