From what I know so far, a slowdown/shutdown in the gulf stream would cause climate change to run counter to the way that it would normally progress (i.e. poles warming faster than the tropics.) Warm water would go around in circles near the tropics, rather than making its way past northern Europe to sink near Greenland, causing the heat content of the tropics to increase disproportionately more at the expense of warming in the arctic.
It's easy to find material that describes how this would affect Europe. Europe would get cooler (or at least not warm as much) and would also get substantially drier. What's harder to find is information on what the effects would be on the weather systems of North America.
What would the effects be on the climate of the gulf coast and eastern seaboard? Would places on the same latitude as Europe such as Newfoundland experience similar changes to the former i.e. cooler and drier?
If I could hazard a guess, I might imagine sea surface temperatures going up substantially year round in the Gulf of Mexico. Bringing in strong blasts of moisture and humidity into the American southwest and interior plains. Hurricanes would get far stronger, and the expansion of tropical koppen climates would extend further beyond the Florida peninsula.
Are there any studies that look specifically into this question? What would be your educated guess as to what would happen to North America's climate?