Beat 1 1/2 cups sugar, butter, shortening, and eggs together in a large bowl until smooth and creamy. Sift flour, cream of tartar, baking soda, and salt together in a separate bowl.

Stir flour mixture into butter mixture; add cream cheese and stir until dough is just-combined. Mix cranberries into dough using a wooden spoon. Cover bowl with plastic wrap and refrigerate until chilled, about 1 hour.

Preheat oven to 400 degrees F (200 degrees C).

Whisk 6 tablespoons sugar and cinnamon together in a shallow bowl. Roll cookie dough into 48 equal-size balls and roll each ball in cinnamon sugar; place dough balls 2-inches apart on nonstick baking sheets.

Bake in the preheated oven until lightly browned but still slightly soft in the center, 8 to 10 minutes. Cool on baking sheets for 1 minute before transferring to a wire rack to cool completely.