It also announced a "vision" to team with partners on a $20 billion upgrade of its long-distance network.
The letter said 18 routes, almost all of Amtrak's long-distance network, were in jeopardy.
The switch, and many others like it along the way, routes the call to its destination over local or long-distance networks.
The company said that it could not keep up with customer demand for its 80-channel optical system, which is used in long-distance networks.
The long-distance network has only 150,000 kilometers of wires and is valued at $40 billion.
Volume, or the minutes of use on Sprint's long-distance network, rose 19 percent.
On a normal business day, the long-distance network handles about 80 million calls.
And since the company did not own its own long-distance network, it had difficulty controlling costs.
No local Bell company is likely to go through the expense of building a long-distance network.
To be effective, a long-distance network basically has to connect to only a single point in each market it serves.