Impeaching Defense Secretary Pete Hegseth would require a simple House majority to bring charges, followed by a Senate trial where a two-thirds vote is needed for removal. How impeachment of Defence Secretary Pete Hegseth would work, from House vote to Senate trial, amid allegations over military actions. By Jan Wolfe WASHINGTON, Nov 10 (Reuters) - US Defense Secretary Pete Hegseth could be impeached by the House of Representatives this week on charges.