One fact working in Ms. Rao’s favor, as she begins her new job, is that there is consensus among politicians and voters of all political stripes that Washington should do a better job streamlining regulations.

But the divide is deeply partisan once the discussion moves to how much regulation is necessary to keep things orderly, safe and fair — and what is deemed a reasonable cost to make that happen. In simple terms, conservatives say the price of red tape has grown too steep, citing a study suggesting that rules cost the economy more than $2 trillion. Liberals say the figures ignore benefits to society.

“Most people do not appreciate the benefits of regulation,” said Sally Katzen, a former administrator of the regulatory office under Mr. Clinton and professor at New York University School of Law. “When asked, they may say they want to get rid of regulations. But which regulations? The stoplight at the intersection? Airbags? Safety barriers at subway stations?”

The regulatory office, commonly known in Washington as OIRA, was created in 1980 as a check on the rules set by regulatory agencies and as a safeguard against ill-conceived regulation. It has usually been staffed with administrators from various corners of academia and the law.

During Mr. Obama’s time in office, some liberals became so infuriated at the slow pace at which regulations moved through the office that they urged abolishing it, calling it the place where “regulations go to die.”

An administrator under President Ronald Reagan, Christopher DeMuth, said special care was needed in weighing regulations, given that there are often “few facts” that decisively predict outcomes. “There are huge uncertainties about what we are doing,” said Mr. DeMuth, now a fellow at the Hudson Institute, a conservative-leaning think tank.

“You think you know what good policy is, but you have to be careful how you do it,” he said. “You can’t just be there ripping out the wiring willy-nilly, or you won’t succeed. You lose the public.”