As a federal investigation into Rudolph W. Giuliani escalates, his advisers have been pressing aides to former President Donald J. Trump to reach into a $250 million war chest to pay Mr. Giuliani for his efforts to overturn the results of the 2020 election on Mr. Trump’s behalf. The pressure from Mr. Giuliani’s camp has intensified since F.B.I. agents executed search warrants at Mr. Giuliani’s home and office last week, according to people familiar with the discussions, and comes as Mr. Giuliani has hired new lawyers and is facing his own protracted — and costly — legal battles... “I want to know what the GOP did with the quarter of $1 billion that they collected for the election legal fight,” Bernard Kerik, the former New York City police commissioner, wrote on Twitter on Sunday. Mr. Giuliani appointed Mr. Kerik when he was mayor of New York. Using expletives, Mr. Kerik added that “lawyers and law firms that didn’t do” much work were paid handsomely, while those who worked hard “got nothing.”