1. Preheat oven to 375°.
2. Wrap outside and bottom of a 9-inch springform pan tightly with a double layer of heavy-duty foil.
3. Place crackers in a food processor; process until finely ground. Drizzle with oil; pulse until combined. Press mixture into bottom and 1/2 inch up sides of prepared pan coated with cooking spray. Bake at 375° for 8 minutes; cool on a rack.
4. Reduce oven temperature to 325°.
5. Place cranberries, sugar, liqueur, and water in a saucepan; boil. Cook 8 minutes or until cranberries pop and mixture is syrupy. Cool 20 minutes. Place mixture in a food processor; process 1 minute or until smooth.
6. Combine 1 cup sugar and cheeses in a large bowl; beat with a mixer at medium speed until smooth. Beat in yogurt, vanilla, and salt. Add whole eggs, 1 at a time, beating well after each addition.
7. Place 2 egg whites in a medium bowl; beat with a mixer at high speed until soft peaks form using clean, dry beaters. Fold beaten egg whites into cream cheese mixture. Pour filling over crust. Spoon cranberry mixture over filling; swirl together using the tip of a knife. Place springform pan in a 13 x 9-inch metal baking pan. Add hot water to pan to a depth of 2 inches. Bake at 325° for 50 minutes or until center of cheesecake barely moves when pan is touched.
8. Turn oven off. Cool cheesecake in closed oven 30 minutes. Remove cheesecake from oven. Run a knife around outside edge. Cool on a wire rack. Cover and chill 8 hours.