I know standard rules of thumb are that it is a good idea to have a liquid emergency fund of between of anywhere from 3-8 months of expenses (depending upon the source). How important is liquidity for such a fund? I recognize it makes sense to have at least some of it available immediately, but this seems like overkill to me. Since "liquid" is not a binary status, would it make more sense to have some sort of tiered or layered system where different amounts are stored at different liquidity levels (so some in a local bank, some in CDs, and some in even riskier, less liquid forms)? If this does make sense, what is a sensible structure for such a system, and if not, why?
EDIT: I did not intend for this question to be specific to my circumstances, but I might have implicitly done so without realizing it. I suppose the main reason for me thinking that having all the money completely liquid was overkill was because I was thinking the main purpose would be more along the lines of loss of income or other drastic changes in life circumstances. I was not thinking so much about major one-time expenses. I'm a single person who does not own his own home, and so with health, car, and renter's insurance, I imagine I personally don't need to worry much about those large, one-time expenses (although perhaps I'm wrong here).