I am a technological ignoramus and cannot provide links. I got the story from a history professor under whom I studied in college. His name was Walter Herrick and before he taught at Quinnipiac College, he had been Chairman of the History Department at Stetson College in Florida.
You may wish to reference the Wikipedia article on the Trent Affair which is overly exhaustive and does not support my story of the cabinet vote. Given today's time constraints, it is the best I can do. Enjoy!