The number of kilowatts you need to generate for running your house off solar energy will depend on how many appliances you use every day. According to the US Energy Information Administration, the average American household will consume 10,715 kWh in a single month.
This converts to roughly 11.647 KW of power. Considering this, it will be very difficult to achieve complete energy independence using solar panels. However, even offsetting 40% of your monthly energy bills can make a significant difference.