McNulty was born in Troy, New York and attended Troy public schools. He attended the La Salle Institute, and graduated from the College of the Holy Cross in Worcester, Massachusetts. He is the third generation of a prominent family in Capital District politics. His grandfather, Jack McNulty, Sr., was chairman of the Green Island, New York Democratic Party from 1919 to 1969, and Michael McNulty's father, Jack Jr., followed Jack McNulty, Sr. as chairman.