Boil a large pot of water. Once boiling, cook the spaghetti according to package directions until al dente. Drain and set aside.
Allow the sauce to simmer gently while pasta cooks. Stir in the softened cream cheese, mixing continuously until fully melted and smooth.
Reduce heat to low and let the mixture cool slightly. Add in the cheddar cheese and stir until fully integrated.
If a thinner sauce is preferred, add a splash of the reserved tomato juice. Otherwise, discard the liquid and stir in the diced tomatoes and cooked chicken.
Fold the cooked spaghetti into the sauce until evenly coated. If your skillet is not oven-safe, transfer the mixture into a lightly greased 9x13-inch baking dish.