While there are many unanswered questions about the amount and nature of the oil in the Gulf of Mexico, scientists do have a detailed understanding of how ocean currents usually work in the Gulf and South Atlantic Bight. The Skidway Institute of Oceanography has a good explanation of this issue.
Experts at the South Atlantic Sea Grant regional physical oceanography summit unanimously agreed that the Loop Current and Gulf Stream would be the main "conveyor" if the oil in the Gulf were to move to South Atlantic waters and shorelines.
In order for the oil to move to the South Atlantic, it first must enter the Loop Current. At present (June 25, 2010), the Loop Current has been "pinched" at its ox-bowed narrowing, creating a large clockwise rotating eddy (named “Franklin”) separated from the actual Loop Current. This eddy has acted as a barrier preventing most of the oil from moving into the Loop Current.
Thus, this eddy is currently acting as a guard against oil reaching the South Atlantic coast. For an animated depiction of the eddy and its relationship to the Loop Current, visit http://omglnx6.meas.ncsu.edu/sabgom_nfcast/, which shows a model developed by researchers at North Carolina State University. There you can review current and past views of the ocean circulation in the Gulf of Mexico.
However, the current eddy will eventually drift either to the west (preventing oil from entering the South Atlantic) or reconnect to the Loop Current (which could allow oil to enter the South Atlantic).
Whether the eddy will drift to the west or reconnect with the Loop Current is somewhat unpredictable, as this is controlled by seasonal weather trends and other, poorly understood factors.
From the standpoint of transporting oil from the Gulf of Mexico to the South Atlantic, the Loop Current /Gulf Stream conveyor belt can not reach the oil spill site as long as the eddy remains in its present position, blocking the northward extension of Loop Current into the Gulf of Mexico.
If the eddy reconnects to the Loop Current, the Loop Current would likely channel the oil toward the Florida Straits and the Gulf Stream.
If oil in the Loop Current reaches the southeast end of the Florida peninsula, it could become captured by the Gulf Stream and move to the north, offshore of Florida, Georgia, South Carolina, and North Carolina. The oil and/or its residuals could move from the Gulf to Gulf Stream waters off Cape Hatteras, North Carolina in about a month's time under typical weather conditions.