Add the 2/3 cup milk, 1/4 cup of the cream cheese, and the next 6 ingredients to a 1-1/2- or 2-pound bread machine according to the manufacturer's directions. Select the dough cycle. When cycle is complete, remove dough. Punch down. Cover and let rest for 10 minutes. Grease 24 muffin cups; set aside.
Divide the dough in half. On a lightly floured surface, roll one portion into a 12x8-inch rectangle. Spread with half of the remaining cream cheese. Starting from a long side, roll into a spiral; seal edge. Cut into 12 slices. Place each slice in a prepared muffin cup. Repeat with the remaining dough and cream cheese. Cover and let rise in a warm place about 30 minutes or until nearly double.
Bake in a 375 degree F oven for 12 to 15 minutes or until golden brown. Transfer to wire racks.
In a small bowl combine sifted powdered sugar and vanilla. Stir in enough milk (1 to 2 tablespoons) to make an icing of drizzling consistency. Drizzle over rolls. Serve warm.