Put rack in center of oven; preheat to 325*F. Coat 9x3 spring form pan with cooking spray. Wrap outside of pan with foil. Combine cracker crumbs and butter. Press onto pan bottom. Bake 6 minutes. Put roasting pan on center oven rack; fill halfway with water.
At medium speed, beat cheese and sugar until smooth. At low speed, beat in next 4 ingredients, until smooth.
Divide batter among 4 bowls; tint 1 yellow, 1 green, 1 pink with red coloring and 1 purple. Pour into pan, one color at a time STARTING with yellow. Gently swirl batters. Place pan in water-filled roasting pan.
Bake 1 hour, 25 minutes until center jiggles slightly. Turn oven off. Let stand in water in oven 1 hour, 40 minutes with door closed. Remove from oven; run knife around edge. Cool and Chill overnight.