Mr. Ellis was a former staff member for Representative Devin Nunes of California, the top Republican on the House Intelligence Committee, and an early member of the Trump administration. He was involved in several high-profile matters, including providing intelligence to Mr. Nunes and putting the reconstructed transcript of President Donald J. Trump’s call with his Ukrainian counterpart in a highly classified computer system.

In November, the Pentagon selected Mr. Ellis, then an official on the National Security Agency’s staff, to become its general counsel, a Civil Service job that does not end with the administration. Trump administration officials had asked the Pentagon’s top lawyer to choose Mr. Ellis, according to people briefed on the process.

Myriad federal rules are in place to try to prevent political appointees from taking permanent Civil Service roles, a practice derisively referred to as “burrowing.” Ms. Pelosi accused Mr. Miller of helping Mr. Ellis burrow in.