I think this one is Creeping signalgrass, also called alexandergrass (Brachiaria plantaginea), but hope some others will chime in.

Carol in Jacksonville

Here is a link that might be useful: Controlling Creeping Signalgrass in Central Florida Lawns

The way the leaves attach to the stem, and the thickness of the stem, I wonder if it's some kind of Callisia. Is it 'juicy' inside?

Take some to your local Agricultural center for proper ID and chemical recommendations.

Are you sure that's not a Dayflower (Commelina)? Does it have blue flowers?

This was nagging at me... I thought my original diagnosis might not be correct. It is not alexandergrass, it is Doveweed (Murdannia nudiflora) (which incidentally, also has blue flowers). This time I am much more certain but of course, if anyone else knows better, please step in and correct!

Carol

Here is a link that might be useful: Doveweed control

If that's what it is, I'd like to have some!!

The truth of the matter is, it doesn't matter what kind of weed you have the important question is......what kind of lawn you have. That's what determines what you can spray. Bayer has a product for St Augustine lawns that you can buy at John Deere stores called, Celsius but it is expensive as it is packaged for commercial use but homeowners can buy it. It is not heat sensitive. Other wise you can wait till daytime temperatures get down to 85 and spray your lawn with atrizine. Spot spraying is also an option during the hot months.