It is by now well recognized how the quantum time evolution for time-dependent Hamiltonians that are quadratic both in position and momentum variables generates ‘‘squeezing.’’ On the other hand, ‘‘squeezed states’’ and their ‘‘high-n generalizations’’ are known to provide a simple classical mechanical description of general quantum time evolution. In this paper, these ideas are combined to show the relevance of ‘‘generalized squeezed states’’ in the semiclassical limit of the evolution of time-dependent wave packets for general time-dependent Hamiltonians, including the multidimensional case.