If it is new, take it back or get the Sears tech to come & have a look.
Of all the big box stores they are the only ones worth a dime and the only ones that stand behind what they sell.
If it is older then get an inline spark tester and watch to see if the spark stops before the engine starts to run down or weather the engine runs down , sparking all the way.
You have then cut the diagnosis time in 1/2 as you have eliminated either fuel or electrics.
The low oil cut out is low volume not pressure so check the oil level is right at the top of the mark, then add another 4 oz, no more.
When the engine spins and oil gets tossed around everywhere the oil level in the sump drops and some time it can be just enough to trigger the switch, paticularly if the unit is sitting on a slope.
Finally is you want more help from this frum we will need the model & code numbers from your engine.