In heavy 2-quart saucepan, mix 1 1/2 cups sugar and the water. Cook over medium heat, stirring constantly, until mixture is clear. Cook, without stirring, to 240°F on candy thermometer, about 10 minutes. Meanwhile, in large bowl, beat egg whites with electric mixer on low speed until foamy. Add cream of tartar and 1/8 teaspoon salt; beat on medium speed until soft peaks form. Increase speed to high; pour hot syrup into egg white mixture. Add marshmallows, a few pieces at a time, beating until stiff peaks form and frosting is thick enough to spread.