In 2006, Morse had a recurring role as Detective Michael Tritter on the medical drama series "House", for which he received an Emmy Award nomination. He portrayed George Washington in the 2008 HBO miniseries "John Adams", which garnered him a second Emmy nomination. He has also received acclaim for his portrayal of Uncle Peck on the Off-Broadway play "How I Learned to Drive", earning a Drama Desk Award and Obie Award. He has also had success on Broadway, portraying James "Sharky" Harkin in "The Seafarer". From 2010 to 2013, he portrayed Terry Colson, an honest police officer in a corrupt New Orleans police department, on the HBO series "Treme". He also appeared in the WGN America series "Outsiders" (2016–17) and in the Showtime miniseries "Escape at Dannemora" (2018).