hmm... I've worked on a lot of old Briggs and Stratton engines. Usually when I have an issue like this, its caused by a lack of fuel. Pulling it over enough times eventually gets it to start pulling gas through the carb properly and run.
Is this an upright (horizontal crankshaft) engine or a vertical crankshaft engine?
Ultimately pictures of the engine would help a lot as there are many variations of these engines, and it would be better to know specifically what variation you have
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'70 107 with k301 engine swap
'71 106 with 38" deck
'70 147
R with factory replacement k321, 42" deck
'61 Original with 38" timed deck
'63 70 "pinkie"
1863 with 54" deck
'46 Farmall H, '50 Farmall Cub
105 x2 (parts)