WASHINGTON (CNN) -- Sen. Chuck Schumer, D-New York, reiterated his position that embattled Attorney General Alberto Gonzales should resign Thursday, and told CNN's John Roberts that President Bush ought to appoint a "non-political" replacement for outgoing Deputy Attorney General Paul McNulty.

"As embattled as the president and the vice president are, it's impossible to say how they would keep him for very long, both on the grounds of credibility and of competence," Schumer said in an interview on American Morning. "And I'll tell you one other thing, when they appoint a deputy attorney general, which they now have to do, it's got to be somebody who is non-political, who appreciates rule of law, and who can run the department, because Alberto Gonzales has none of those things."

Citing personal reasons, former Deputy Attorney General Paul McNulty submitted his resignation Monday.