Cadwalader, Wickersham & Taft struck a deal with President Trump last month intended to secure the future of New York’s oldest law firm. Instead the pact is backfiring, adding to an exodus of lawyers that has placed the firm on uncertain footing.Cadwalader already was facing troubles, including imminent attorney departures, before its April 11 deal with the White House in which it avoided a punitive executive order by pledging at least $100 million of pro bono work to support the president’s priorities. The agreement now is pushing more lawyers to leave, people familiar with the matter said, spurred by anger that the firm capitulated to Trump instead of fighting back against an administration campaign that many in the industry believe to be unconstitutional.