Amazon has a very long way to go to be a true threat to UPS and FedEx as a common carrier, but they will be a fly in the ointment. Amazon most likely will target small shippers who do not enjoy big discounts with FedEx and UPS, these are the most profitable packages. They won't handle over 70lb packages due to USPS weight limit and will not target large packages as they don't fit in cars. They will deliver the metropolitan/city packages and have USPS deliver the rural packages. They will reduce their dependence on the USPS as density increases in those areas. As they slowly build their density, then they will be a major threat to UPS and FedEx.
As Amazon ramps up their delivery service, they will not deliver, i feel, the same way UPS and FedEx do. It will be a different model, I fell they will have waves of vans and cars every few hours going out to deliver in the cities versus UPS and FedEx that go out once a day. Right now, if a trailer arrives at 1:00 pm at UPS or FedEx, it waits for delivery the next day, Amazon will deliver it the same day. Amazon could have later cut times and go further in less days than UPS or FedEx.
Amazon cares about lowering their cost of delivery of their packages and will subsidize their delivery cost with other shippers packages. Amazon has the luxury of not starting out as a delivery company and depending on volume to grow. They can cherry pick the most profitable packages and let UPS and FedEx fight over the lower revenue packages. If it becomes profitable to deliver packages as if it were a stand alone company, watch out UPS and FedEx.