Craftsman lawn tractor 917.271060w/kohler 15.5 hp engine cranks but backfires thru carb and wont start.

check the solenoid on the bottom of the carb check for movement and power if it moves and has power open the carb and clean it

The timing is controlled by the key in the top of the crankshaft locating the flywheel. If this is sheared the engine will either run rough, backfire, pop or not run depending on how badly the timing is out.

The key sheared on flywheel. Remove shroud and unscrew nut, then check for bad key.
Next, valves not closing right.
Next, carb. fuel mixture to rich.

suggest to look at the carb adjustement unscrew

Look at this tip I wrote on the no start problem.

The carb. needs to be cleaned. Pay extra attention to the high speed circuit.

sheer pin on engine shaft is busted. take off the fly wheel and look inside or on the shaft.

Do you have a Briggs or kohler engine.I am having the same problem.I have changed the fuel filte, fuel pump, and cleaned the carb.Sears has been no help at all.The reason I ask about the engine you have is that people are having the same problem no matter what engine they have.So therefore it probably is not the engine so it is something else on the mower.My mower runs fine for about 10-15 then starts to stutter and backfire.I am continuing to pursue this problem and I will post back here if I come up with anything.

For a small gas engine than won't start, think FAST -- Fuel, Air, Spark, Timing. You've replaced the filters and spark plugs and squirted in some starter fluid, eliminating the simple common fuel, air, and spark problems -- but I because of the backfiring I think your problem is in the timing -- like a sticking valve. Probably more than you want to tackle at home, but might not be as expensive as an engine replacement. Take it to a good small engine mechanic -- best bet is a lawn equipment shop that has been around many years. Drive a little farther to get to one if necessary.