I do not believe that 12 hours is sufficient notice for temporary parking signs. My guess is, absent an emergency, the city may take it in the shorts on this one - or, at least for the initial costs. Provided, of course, the posting of the tow away signs was improper.
Here are the relevant sections for impound authorities on temporary signs pursuant to CVC 22651:
(l) When a vehicle is illegally parked on a highway in violation
of a local ordinance forbidding standing or parking and the use of a
highway, or a portion thereof, is necessary for the cleaning, repair,
or construction of the highway, or for the installation of
underground utilities, and signs giving notice that the vehicle may
be removed are erected or placed at least 24 hours prior to the
removal by a local authority pursuant to the ordinance.
(m) Wherever the use of the highway, or a portion of the highway,
is authorized by a local authority for a purpose other than the
normal flow of traffic or for the movement of equipment, articles, or
structures of unusual size, and the parking of a vehicle would
prohibit or interfere with that use or movement, and signs giving
notice that the vehicle may be removed are erected or placed at least
24 hours prior to the removal by a local authority pursuant to the