The number they are using came specifically from the number of mariners needed to man the reserve fleet. There was a thread about it here:
A recent report to Congress identified the need for 13,607 qualified mariners for sustaining the mobilization and commercial operations concurrently under highly optimistic assumptions of no loss of life or property. The identified pool of mariners will therefore provide three to four months of force projection support at best, taking into account the necessary crew rotations.
This is from the OP:
In the past several decades, the number of United States merchant mariners with unlimited oceangoing credentials who have sailed in the last 18 months has dropped below 12,000**. According to estimates from the Department of Transportation, if the United States entered into a large-scale conflict that required the military’s full mobilization, we could fall short of the number of mariners needed to sustain contingency operations**