Mr. McGahn has spent most of his professional career in Washington, unusual in an administration that has largely kept out Beltway insiders. His wife, Shannon McGahn, is the staff director of the House Financial Services Committee. But over the years he developed an unusual image for a conservative, growing his hair long and playing guitar for a rock band that specialized in 1980s cover songs until he had to focus on working for Mr. Trump. That background dovetails with a policy record that is more libertarian than classically conservative. His specialty is election law, and at the Patton Boggs law firm, he worked under Benjamin Ginsburg, a veteran Republican campaign lawyer, defending clients against Federal Election Commission investigations into coordination between Republican campaign committees and outside groups. President George W. Bush appointed Mr. McGahn to serve as a commissioner on the Federal Election Commission, where he developed a reputation for unabashedly trying to stop what he believed were its regulatory excesses. After leaving the agency, he and Mr. Ginsburg left Patton Boggs for another firm, Jones Day. Mr. McGahn has played little role in dealing with the Russia investigation because the White House brought in outside lawyers — first Marc E. Kasowitz, and now Ty Cobb — to handle it. Mr. McGahn has told some friends and colleagues that he has considered resigning over the past six months, but that Senator Mitch McConnell has repeatedly urged him to stay.