The expression "Wacheschieben" is well-known to native speakers. It's synonymous to "Wachestehen".
I just realized that this word can be confusing to language learners.
Ich habe vier Wochen hintereinander jeden Sonntag Wache geschoben.
The resulting question is: what does it mean to "push", in this case?
Same applies to, for instance, "Nachtschicht schieben". To push[sic] night shift?
Well, all I can say is that schieben in Wacheschieben has nothing to do with to push. (Though, to push has quite a huge set of meanings so I wouldn't be surprised if a similar sense is covered by the English word as well.)
I did a quick search, but the information I gained from Grimmsche Wörterbuch, DWDS, Duden and Wiktionary were more than just disappointing. Most of them do not contain a definition, let alone some hints on the etymology.
So the question that raised: what does schieben mean in this context? Where does it come from?
The only idea I can come up with is that it is related to definition 3 in Wiktionary:
 jemand für etwas verantwortlich machen
Sie schoben die ganze Schuld auf ihren Vorgesetzen.
When someone is in duty, the responsibility is "pushed at him".
However, this appears to be unlikely to me. So, again: why do we say that?