A business owner in the UK wants to hire me, a US citizen. He has submitted the sponsorship request, and we are eagerly awaiting a response. Assuming he is successful, how long should it take for me to get the visa once he provides the Sponsorship ID?
Once a certificate is issued, the process dissolves into a very standard entry clearance application. As mentioned in comments, you can examine the turn-around times for Americans here.
If you are in a real hurry you may be able to qualify for a premium service. They are very flexible and have premium packages up to GBP 15k, plus a lounge for your chauffeur.