Abraham enlisted in the Haitian army as a young man. He rose to the rank of lieutenant general and became one of the few military members in the inner circle of President Jean-Claude Duvalier. Abraham supported the 1986 coup against Duvalier, and served as foreign minister for the first time under Henri Namphy from 1987 to 1988.
Abraham became acting President of Haiti on March 10 1990 after street protests forced President Prosper Avril into exile. Abraham gave up power three days later, becoming the only military leader in Haiti during the twentieth century to give up power voluntarily. Abraham helped to crush a coup attempt by Roger Lafontant in January 1991.
In 1991, Abraham retired from the army and moved to the United States. He settled in Miami, Florida and drifted into obscurity. He lived near another former Haitian politician, Gérard Latortue, who would later become prime minister. In February 2004, Abraham made a radio address from Florida calling on President Jean-Bertrand Aristide resigned.
After Aristide's resignation, a new government needed to be formed, and some believed that Abraham would become prime minister. Latortue was eventually chosen for the job, and invited Abraham to return to Haiti and become interior minister. Abraham served in that position from March 2004 until a January 31 2005 cabinet reshuffle, in which he became foreign minister.