WASHINGTON — It was a typically hectic day for William A. Burck as he juggled the demands of managing one of Washington’s premier white-collar law firms while he was in Paris for meetings on behalf of a corporate client facing corruption charges.

But that was not all he was trying to manage from his room in a hotel near the Champs-Élysées last Wednesday. Part of the time he was on the phone dealing with the legal and political fallout from the abrupt dismissal that day of Donald F. McGahn II, the White House counsel, one of at least a half dozen of his clients who work for President Trump or once did.

And part of the time he was signing off on the release of a final batch of documents related to the time that Judge Brett M. Kavanaugh, Mr. Trump’s Supreme Court nominee, spent as a senior aide in the George W. Bush White House. Hired by the former president, Mr. Burck supervised a team of lawyers that examined thousands of documents, a process that has been bitterly criticized by Democrats, who say Mr. Burck is an administration ally and longtime Kavanaugh friend who cannot be trusted.

Democrats hope to use the fact that Mr. Burck oversaw a process that led to the withholding of more than 100,000 pages of documents to argue that they know too little about Judge Kavanaugh’s record to move ahead with his confirmation hearings on Tuesday.