The allegations against Sen. Robert Menendez may have started with unsubstantiated stories about trysts with prostitutes, but questions about the lawmaker’s conduct have reached the point where they’re not focused on sex. A slow drip of national news reports about the New Jersey Democrat and his ties to Florida ophthalmologist and political donor Salomon Melgen have put his office on the defensive over an assortment of issues including a port contract in the Dominican Republic and a possible intervention in a Medicare billing dispute involving the doctor. Menendez tried to move forward with his normal agenda Thursday, holding a morning...