The only way you will know for sure is to try it. The problem will be voltage drop due to current.
The voltage in the house could be anywhere between 127 and 115 VAC. This will depend where the house is on the power company's distribution feeder. If it is 127 you should have no problem, but watch the connectors for heating. If it is 115 vac you will likely have a problem that no "reasonable" sized cord will help with.
Don't worry about the short run of #14 wire in the house. It should be rated to the circuit breaker and will carry the current. The length with respect to voltage drop will be short.
Also, the incoming voltage to the house can vary with time of day. In areas where there is heavy load on the feeder from heating or air conditioning, the voltage can drop when the load is highest. This is why some appliances can have trouble only at certain times.
If you do use an auto transformer be sure it has good control and voltage monitoring. If you installed a fixed type as nd set it to boost when incoming voltage is low and ac running, it could be too high at some other time. Electronics will fail, frequently, at 132 VAC.
