According to the Oxford English Dictionary, early usage refers to lines that do not move, such as one used in angling. Slightly later American usage refers to a boundary in a prison which prisoners must not cross. There is only indirect evidence that the sense of "due date" may be connected with this use of the term in prison camps during the American Civil War, when it referred to a physical line or boundary beyond which prisoners were shot. In 1904, in a report from the US Department of Commerce and Labor, the term is used for "minimum work goals" (and in contrast to bonus line): for example, as a typographer the line could be 18,000 ems per day; should one not cross this line, then that could have negative consequences. In 1917, the term is attested as a printing term for a guideline on the bed of a printing press beyond which text will not print. Three years later, the term is found in print in the sense of "time limit" in the closely connected publishing industry, indicating the time after which material would not make it into a newspaper or periodical.
1
A time limit in the form of a date on or before which something must be completed.
I must make this deadline or my boss will kill me!
TfW's [Transport for Wales] plans to meet the PRM [Persons with Reduced Mobility] deadline and withdraw all Pacers by 1 January have been made more difficult by delays to introduction of Class 769 and 230 units.2019 October, Rhodri Clark, “TfW seeks PRM derogation for Class 37 sets”, in Modern Railways, page 87:
2
Archaic A guideline marked on a plate for a printing press.
According to the Oxford English Dictionary, early usage refers to lines that do not move, such as one used in angling. Slightly later American usage refers to a boundary in a prison which prisoners must not cross. There is only indirect evidence that the sense of "due date" may be connected with this use of the term in prison camps during the American Civil War, when it referred to a physical line or boundary beyond which prisoners were shot. In 1904, in a report from the US Department of Commerce and Labor, the term is used for "minimum work goals" (and in contrast to bonus line): for example, as a typographer the line could be 18,000 ems per day; should one not cross this line, then that could have negative consequences. In 1917, the term is attested as a printing term for a guideline on the bed of a printing press beyond which text will not print. Three years later, the term is found in print in the sense of "time limit" in the closely connected publishing industry, indicating the time after which material would not make it into a newspaper or periodical.