Born in Ireland, Fr. Dempsey was ordained a priest in 1891 and came to America to serve in the Archdiocese of St. Louis. He soon became known for working with less fortunate men. He opened a hotel in 1906 for working men, another in 1911 for working women and, in 1922, a third for African American workers. During the Great Depression, he operated "Father Tim´s Free Lunch Room." He frequently was called on to mediate labor disputes and it is believed he intervened in at least 50 strikes. He established the White Cross Crusade in 1922, which provided food for children and supplies for their parents.

In 1909 he purchased a large section of ground in Calvary Cemetery and named it "Exiles Rest" after his first hotel so that the "boys" who had no families could be buried in consecrated ground. When he died, he was buried with 226 of his "boys." His charities still exist today.