In April 2012, Garcia received the Teacher of Peace Award from Pax Christi USA, a left-leaning Catholic peace organization. Past winners include journalist and peace activist Dorothy Day, actor Martin Sheen, poet and priest Daniel Berrigan, and "Dead Man Walking" author Sister Helen Prejean. Garcia now tours the country and speaks every year at 20 to 25 universities, churches, and other organizations that help immigrants.
He was inspired to seek out the "poorest of the poor" when Mother Teresa visited El Paso. She wrote in a letter to him, "Now you will announce the good news and bring the people home to Jesus" – hence the name Annunciation House.
In the early years, the "poorest" were undocumented Mexican immigrants. In the mid-1980s, Annunciation House began to also concentrate on Central American immigrants fleeing violence in their countries.
Since 2008, the house has placed a renewed focus on refugees from Mexico, especially victims of the calamitous violence in Ciudad Juárez, just across the border from El Paso. For about four years the house has sheltered 80 to 90 of these "guests" at any given time.
Cristina Parker, communications director of the Border Network for Human Rights in El Paso, says that the people of El Paso are "not touched directly by the violence in [Ciudad] Juárez, but we're touched emotionally. Where Annunciation House makes a difference is in bridging the gap in a healing way."