Briggs Model 311707 Craftsman lawnmower won't stay running?

I have a Craftsman lawnmower with a Briggs model 311707 17.5 hp motor that wont stay running. I just changed the starter, the air filter and the muffler. At first it wouldn't start at all so I took the carb off and cleaned everything out and made sure the fuel solenoid was working. I then drained all the gas and replaced with fresh. I pulled the plug cleaned and checked the gap. After all of that it would start, run for a couple seconds, chugging, then stop. If I held my fingers over the carb to choke it, it would fire up and I could get it to almost idle like that, but as soon as I take my fingers away, it stops. It's getting fuel, but it doesn't seem like enough. I'm stumped. Any Pro's out there have an idea?