Here is the current upper level situation. NOTE the location of those 500mb winds today. This will be worth noting in latter portions of the post.
Again, above is the upper level flow for today high high up there. See the low/trough to the West of Florida by Cali? This low will gradually be moving east, but now guidance shows it never quite clears Florida through mid-month. Instead, NOTE THE NW CORNER of the image. Another Low is moving in.
The low toward the NW U.S., now, is forecast to drop in behind the trail left by the first one, and carve a broad upper level trough along and east of the Mississippi in the next week to 10 days. There will be at least two more frontal boundaries to contend with during this process, the first being late Thursday as the one of today dissolves.
WEDNESDAY: Wednesday looks similar to today, but possibly a bit even warmer aloft in the mid-levels. Coverage difficult to ascertain, but expecting something similar to today, with little chance of severe or even strong storms as it stands now. Today will be a good test to see what does occur in the long run though. Never say never when it comes to boundary collisions is the key.
THURSDAY: As we can see, upper level trough and winds aloft now moving in, with a surface front (not shown) moving down the state. Convergence along that boundary, sea breezes, and cold air aloft could make for another day like Monday was only more active along the immediate East Coast.
THURSDAY: Possible stronger to severe storms on Thursday from Volusia and South along the east coast ahead of a frontal boundary.
FRIDAY/SUNDAY: Easterly winds manifest, breezy and dry, but with clouds and possible showers toward the Keys and Southern Dade, but pleasant otherwise. Front will be way south, but remain in the mid-levels. In a sense, so far, it could 're-manifest' by Late Sunday..moving back north..with rain south of Volusia along the coast in doing so.
Monday/Tuesday time frame could be stormy or rainy along the east half of state, with the Latest GFS showing up to 2" of rain if not more in this area. That is a 'new one" though and too far out in time to hold fast on to.
BEYOND: Time will tell, the all in all though is that this pattern for this time of year is fairly rare from my recollections...as the amount of coverage reflects late June, with showers possible toward the third week at various times.