NEW YORK—The killing of Osama bin Laden could indeed be a "watershed moment" in the long-running war on terror, but will likely be a wash for the sinking U.S. dollar.

With jubilant crowds gathered at Ground Zero in New York, the dollar isn't joining the celebration: It is still weighed down by easy-money policy that isn't going to change based on the take-down of al Qaeda's leader.

"If...