A prominent Washington lobbyist close to Kevin McCarthy, the House minority leader, is warning Republican political consultants that they must choose between working for Representative Liz Cheney or Mr. McCarthy, an ultimatum that marks the full rupture between the two House Republicans. Jeff Miller, the lobbyist and a confidant of Mr. McCarthy’s dating to their youthful days in California politics, has conveyed this us-or-her message to Republican strategists in recent weeks, prompting one fund-raising firm to disassociate itself from Ms. Cheney, a Republican from Wyoming. In response, The Morning Group, a fund-raising firm she hired to help prepare for a...