Cutting back on my food intake is difficult.  Won't exercising more help create a bigger daily calorie deficit by increasing the amount of calories my body needs to maintain each pound of weight?

Only to a limited extent.  Moderate exercise, as I described previously, generally is associated with a caloric requirement of 10 calories per day to maintain each pound of weight.  Increasing the time and intensity of exercise may increase the body's calorie requirement a little bit but not on a 1: 1 ratio.  The body's metabolism becomes more efficient with greater exercise, and the calories required to maintain 1 pound of weight follows another law of diminishing returns with more intense or more prolonged exercise.  I usually tell my patients that the most that the most useful thing that spending 4 hours in the gym 3 days per week instead of 1 hour 3 days per week accomplishes is keeping a person away from the dessert table for a longer period of time.