In a bowl, with an electric mixer on medium speed, beat butter and 1 1/2 cups sugar until smooth. Beat in 2 eggs, pumpkin, and 1/3 cup water until well blended, scraping down sides of bowl as needed. In another bowl, mix flour, cinnamon, baking soda, baking powder, and nutmeg; stir or beat into butter mixture until well blended. Spread batter evenly in a buttered and floured 10- by 15-inch baking pan.
In a bowl, with an electric mixer on medium speed, beat cream cheese, remaining egg, and remaining 1/4 cup sugar until smooth.
Drop cream cheese mixture in 24 evenly spaced 1-tablespoon portions over batter. Pull a knife tip through filling to swirl slightly into batter.
Bake in a 350° oven until center of pumpkin batter (not cream cheese mixture) springs back when touched, about 30 minutes. Let cool completely in pan, then cut into 24 bars.
Note: Nutritional analysis is per bar.