If you cluster at the time level, you are imposing that a units errors are uncorrealted with itself in different periods. For example say states and time, if you cluster at the year level, then there is arbitrary correlation among states within a year, but you are imposing no correlation between errors of Maryland say, in year one and two and so forth. I think that is a little harder to justify than clustering at the state level.

But you read about multi-way clustering, see this paper (pdf warning). For example they try to address the problem when:

“In a state-year panel setting, we may want to cluster at the state level to permit valid inference if there is within-state autocorrelation in the errors. If there is also geographic-based spatial correlation, a similar issue may be at play with respect to the within-year cross-state errors (Conley 1999). In this case, researchers may wish to cluster at the year level as well as at the state level.”