Beat 1 ½ 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°F (200°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.