I saw millions of ladybugs today that obviously mass-hatched. They were all headed somewhere, although none seemed to land on anything. Does anyone know how long these hatchings last? Is it hours or days?

Wiki does.

 

 

http://en.wikipedia.org/wiki/Lady_bugs

Most coccinellids mate in spring or summer and the female lays a cluster of eggs (numbering from a few to a few hundred, depending on species) as near as possible to an aphid colony. In most species these eggs hatch into a larval state within a week. This state lasts 10–15 days, and they then go into a pupal stage before becoming an adult coccinellid. The entire life cycle of the Coccinellid is only 4–7 weeks. Most ladybird species are univoltine, producing only one generation a year, although some are bivoltine.