Obviously, driving doesn't spread COVID-19 on its own. It is, however, an accurate proxy for overall changes in behavior.
Florida had a decreasing case count in April, when their driving was about 60% below baseline. Sometime in early to mid May, infections started to increase (visible in the graphs about two weeks later). That was at about 30% below baseline.
Recently, Florida's driving has dropped back to baseline, but is still far above the May level that led to a flat case count. Given this data, and the fairly modest steps taken by the Governor, I suspect true cases in Florida are flat or still rising today, even with increased mask use. (And discounting today's reopening of Disney World!)
My sense is that some combination of closings or citizen behavior will need to decrease about 30% from today's levels to get back to a sustained decline. That's about half the depth of the original lockdown, but they're nowhere near that today.
Texas is in a similar position, maybe a bit closer than Florida, but probably still in slow growth or flatline territory today. Significant progress will probably require tighter restrictions on restaurants, churches, etc. AND a sustained increase in mask use.
With current policies and behaviors, I'd expect Texas to see its case count level out at a high level over the next week or two, with death counts rising for at least the next 3 weeks.