Im a big believer in the "comprehensive emergency / big purchase" cash fund.
It should be able to cover any of the 2 biggest possibilities:
1) purchase of a vehicle (min $5000, could also be as a repair bill)
2) your health insurance out of pocket maximum
3) coverage of the combined deductibles for your renters/homeowners/car insurances ("you crash your car into your house"). A nice side effect of having a big emergency fund = you can carry higher deductibles and pay alot less in insurance, allowing you to invest more).
4) large ticket house item going down (roof, A/C, heating) or your place catches on fire / floods / tornado / total loss (big evac fund), min $5,000... even for renters. Yes you may get paid back, but not immediately.
5) no job for 3 months (take what you need to live w/o investments, make sure to ADD what COBRA will cost you!, do not count on UI).
6) no income for 3 months (repeated twice intentionally, so that it covers a short job loss and one other disaster, or just a long term job loss).
7) cost of a good lawyer if you get into a little legal trouble, I say $10,000, but if you are a more 'spirited' type... more!
Figure the numbers for #1 - #7 and add the two biggest ones together, that should be your emergency fund size. Odds are more than 2 of the above disasters will not strike in the same year. Any use of emergency fund: when the event is over, no investing until this fund is recharged.
So, with that in mind, I definetly dont think short term money should be invested, you have this stockpile of cash set aside to cover a car, or many other disasters. Nowadays it can earn 2% which isnt too terrible for money with instant access. THis also allows you to safely invest the rest, knowing you wont need it for a LONG time.