According to the current forecast track, Fay is projected to come ashore in the Naples-Ft. Myers area of SW Florida on Tuesday morning, move up the west side of the state passing between Tampa and WDW, and be somewhere around the Gainesville area by Wednesday morning.
If that track holds true (which it probably won't), the heaviest time for WDW would be Tuesday afternoon/evening. The storm would be west of WDW, which means WDW would be in the right front quadrant of the storm which is usually where you find the heaviest weather.
If this pattern holds, Tuesday will be a lost day with a lot of wind and rain. Nobody will be in any danger as long as you stay indoors, but it will be an ugly day.
After the storm passes, the weather usually clears up, and Wednesday could be the prettiest day of the week at WDW.
Keep in mind, however, that these projected tracks are VERY tentative this far out. The error factor for this storm has been 225 NM (261 miles) four days out and 300 NM (348 miles) five days out. That is a HUGE variance, so we really have no idea where this thing will be on Tuesday at this point. It could just as easily be 100 miles west of Florida in the Gulf or 100 miles offshore in the Atlantic on Tuesday.
Given the unpredictability of this system, I don't think we'll have a very good idea where it is really going until Sunday night, or even Monday morning.