Preheat oven to 375°.
Wrap outside and bottom of a 9-inch springform pan tightly with a double layer of heavy-duty foil.
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.
Reduce oven temperature to 325°.
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.
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.