Bacteria grows on most foods that are under 140 degrees and over 36 degrees. Some food is ideal for growing bacteria at room temperature and there can be billions of bacteria after several hours. Yes, it is possible to get sick from eating food that has been left out for a day.
Depends on what is being left out. The so-called "danger zone", the temperature range which is optimal for the growth of food-borne pathogens, is between 40and140 degrees Fahrenheit. Anything left out for more than a few hours is no longer safe to eat, especially things like meats, seafood, and starches. Eating things left out for days is more than risky, its reckless...especially if a child is eating it too.