“If O.M.B. does not stand down from its attempt to prevent designated agency ethics officials from responding to the O.G.E. data call, we will seek the waivers directly ourselves,” the letter from the senators said. “The administration certainly cannot dispute that Congress has the right to this information.”

Ethics watchdogs, as well as Democrats in Congress, have expressed concern at the number of former lobbyists taking high-ranking political jobs in the Trump administration. In many cases, they appear to be working on the exact topics they had previously handled on behalf of private-sector clients — including oil and gas companies and Wall Street banks — as recently as January.

Mr. Shaub, in an effort to find out just how widespread such waivers have become, asked every federal agency and the White House to give him a copy by June 1 of every waiver it had issued. He intends to make the documents public.

Federal law gives the Office of Government Ethics, which was created in the aftermath of the Watergate scandal, clear legal authority to issue such a “data request” to the ethics officers at federal agencies. This is the main power the office has to oversee compliance with federal ethics standards.

It is less clear whether it has the power to demand such information from the White House. Historically, there has been some debate over whether the White House is a “federal agency” or, as it calls itself, the “executive office of the president.” Such an office might not be subject to oversight.

The White House, however, tried on Wednesday to stop the process across the entire federal government, even before most agencies had responded to Mr. Shaub’s April 28 request.

“This data call appears to raise legal questions regarding the scope of O.G.E.’s authorities,” said the letter, which was sent to Mr. Shaub by Mick Mulvaney, the head of the Office of Management and Budget. It continued, “I therefore request that you stay the data call until these questions are resolved.”