There is a case for due diligence before a terms sheet and also after. Ideally, it makes sense to do some beforehand. But if you are dealing with many potential investors at a time, it may not make much sense to invest extensive time until first finding out if you will even be able to reach mutual terms in the first place. There are various levels of due diligence, and depending on scope and type of the investment more or less may be needed.
The biggest issue I have seen with terms sheets and LOI's is the entrepreneur puts way too much stake that the deal is going to happen. Until you have a long form contract signed and money is in the bank, there is no money as others have alluded to. If you are to terms sheets certainly be positive and optimistic, but don't let it derail your pursuit of any and all investors. Not to mention if you have several potential investors that gives bargaining options. With this though, I am speaking more with regard to private investors, not institutions.