My Craftsman Mower Fires Up When I Push The Primer A Couple Of Times And Then Immediately Dies. What’s Wrong?

I have a Craftsman rotary push-type mower with a 4.5 HP Briggs & Stratton engine. I tried to start it today after about 6 months of disuse. I had left a little fuel in the tank over the winter. The engine fires up for a couple of seconds after I push the primer a few times and then immediately cuts off. I have replaced the fuel (though did not completely drain it). What could be the problem?