The guidance models are in agreement that a positively-tilted, upper-level trough will amplify throughout the night. This trough is expected to push towards the east Tuesday. Models are also showing 850-mb winds blowing decently out of the southwest - as high as 35 knots - and will aid in warm air and moisture advection to Florida. There is also a chance of having enough sunlight to help destabilize the atmosphere further. The SPC notes in their outlook that vertical wind shear will increase as the trough approaches from the west.
The primary threat appears to be strong damaging winds and a risk of tornadoes. Bow-echoed thunderstorms can influence this threat. The timing appears to be very late afternoon to after dusk.
I'll do my best to write a blog post tomorrow afternoon to give another update on the situation in Florida. Keep an eye on my Twitter feed (@daweathaman) for the latest. Stay alert, my Florida friends.