I'd bet that 99% of these signs that say they can close in 48 hours are nothing but "puffing". Exaggerated advertising to draw people in. Just like restaurants that say "best fried chicken in the state" or bars that say "coldest beer in town".
From a signed contract to closing, assuming no lenders (even hard money) involved, you probably could do it in Justin's timeline. As soon as you start having to find a buyer, its going to take longer. If that buyer's using any sort of loan against the property, even hard money, then you're looking at an appraisal, title reports, etc. If everyone involved in a hard money deal is moving quickly, you might close in a week from the time when you have a fully signed contract. If conventional lenders are involved, figure a minimum of a month.
So, if you're wholesaling, you need to know your buyers. If you have honest to goodness cash buyer's and you've found a house that exactly meets their buyer's criteria (that is, you can call your buyer as you walk out the door and KNOW they will say yes), you can close in a matter of days.
OTOH, a house about six houses up the block from me was picked up by one of our big local wholesalers. He moves quite a few properties. It languished in his inventory for a month before he dropped it. It eventually sold a couple months later as a HUD to a owner occupant. So, no guarantee you can find a buyer at all.
If you're just starting, and don't have the cash to close deals yourself, I'd avoid making any promises.