Hudson has been an influential adviser to President Bush and a close friend of the White House political strategist Karl Rove since the late 1990s. Hudson first caught Rove's attention by publishing a study in Crisis in 1998 arguing that Republican candidates could make inroads among traditionally Democratic-leaning Catholic voters by focusing on regular churchgoers, a strategy that dovetailed with Bush's emphasis on "compassionate conservatism."

Hudson signed on as an adviser to Bush's 2000 presidential campaign. For the last four years, he has been a prominent participant in a weekly conference call held by the Republican National Committee each Thursday with influential Catholic supporters.

William Donohue, president of the Catholic League for Religious and Civil Rights, said Hudson has played an almost indispensable role reaching out to Catholics for the White House.

Donohue said Hudson's resignation will inevitably set back the Bush campaign's efforts with Catholic voters. "He was the ultimate networker," Donohue said. "I think it will be hurt because of the ties that Deal had."