That is not to say that the system couldn't go stationery off shore even longer than any of the models indicate, but for now, it appears no matter where it ends up in 48 hours, agreement is that it lifts north and east generally tracing the U.S. East Coast. The better agreement comes in the extended. Once the low departs the SE. U.S. (assuming it does in the next 72 hours), high pressure ridge to build in across South Florida in general putting most of the state in a SW or W flow aloft, which favors the east side for thunderstorms later in the day once we return to status quo for summer.
TODAY: Chance of a few isolated stronger storms after 6pm through 9 pm as shown. Though it does not look like there will be a good sea breeze convergence today, therefore, anything 'strong' might be hard to come by especially since temperatures aloft have warmed a bit and we need cold air aloft to generate the stronger activity. Most rains will fall today along to west of I-95, though will watch for some coastal showers possibly to impinge upon east central toward or after dark and overnight depending on what happens with the low.
:NOTE: The more wrapped up (or stronger /organized) any low pressure will get to the east of Florida, the drier the forecast becomes (unless it actually moves fully on shore).