According to the GFS model, anti-cyclonic flow from a ridge at the 200mb level, anticipated to develop out of Bermuda SW through FL, will carry him NW into Gulf of Mexico. Simultaneously with this, an upper level trough is anticipated to intensify and dip deep into Mexico. The cyclonic wrap-around flow of this trough at the 200mb level in conjunction with the continued anti-cyclonic action of the Bermuda ridge will pass him NW into the open Gulf. However, he will begin to experience significant shear as he continues his NW motion over the coming days. The maximum 850-200mb shear differential will be in excess of 70kts from Louisiann to his north, east to Florida, and to lesser amounts turning south (east of Florida's east coast) all the way to south of Cuba (Haiti?). This shearing will amount to 270 degrees circumferance of the storm for a significant part of its lifetime, and should rob the storm vital energy to become a monster. GFS suggests that the he could hit New Orleans Monday morning (7 AMish) with about 45 kts max sustained.
NOGAPS, on the other hand, suggests a different scenario. The Bermuda high (at 200mb level) will hem him in (south of Cuba) until Friday night (when the upper level Bermuda high is modeled to diminish somewhat). At that time, the wrap around winds of an intensifying trough at the 200mb level decending through TX & into Mexico, and expected to curl up through the Yucatan Peninsula, will steer him towards Florida. This model shows he would be about 100 miles off Tampa coast by Saturday night (winds could be as high as 45mph in Orlando & Talahassee). However, the Bermuda high is shown to reestablishing itself by this time, and would push him back into the gulf (towards Mississippi). According to NOGAPS, he would then make landfall between Pensacola & E of New Orleans by Monday morning (7 AMish) with about 35kts sustained (and pretty much fall apart at that point).
Its all going to depend on what the Bermuda high does. One way he wears himself down on Florida (even so he never makes landfall there), the other way he goes out into the Gulf, but gets robbed due to significant shear (and never can develop despite open gulf environment). If he does the latter he's going to dash himself to pieces onto Louisiana (he'll go NW from New Orleans trying to get to Oklahoma, but steering winds from the TX-Mexico trough won't let him get there.
I think I have just had my first flash back looking at that...