Alligator Weed (Alternanthera philoxeroides) is listed as a Florida Category II non-native invasive and found in much of the state:
http://www.freshfromflorida.co...
http://florida.plantatlas.usf....
I lean toward Danita's ID of Gomphrena serrata. My Florida Wildflower book shows the common name "Arrasa Con Todo" which apparently translates from spanish to "Destroys Everything"
but it also shows another often called name of "Prostrate Globe Amaranth". It's not a Fla. native but has become naturalized along the Gulf and Atlantic coasts, inhabiting open, sandy sites and along roads and sidewalks. It also states that it's considered a nuisance weed in lawns and I believe I've seen it in my lawn in the past!
http://florida.plantatlas.usf....
Found in much of the state:
http://florida.plantatlas.usf....
My Florida Wildflower book also shows two others Alternanthera flavescens (Chaff Flower) and Alternanthera maritima (Beach Alternanthera) but they seem to have different growth habits.