Really messy floors? So gross that you're worried you might have to get down on your hands and knees and actually scrub? Try the Crappy Housewife Patented Sloppy Mop Technique*.
First, mop your way across the room without wringing out the mop. Your floor will be sopping wet, so make sure you don't slip and fall. (Bonus Tip: Do this job in bare feet, and scuff the bottoms of your feet a few times across the mop to clean them so you don't leave dirty footprints.)
Once the floor is sopping wet, go back to the other side and work your way across with a really well wrung-out mop. Almost all of the dried-on gunk will come up easily on the second pass. Stick a spatula in your pocket as you go, and use it to scrape up any rogue crusty bits.
*not actually patented