The Vendor is usually keen to get in front of the people responsible for the selection. The vendor has an agenda which involves showing you what the vendor wants to show you and not showing you the weak points of the software. You need to take charge and make sure you see what you are interested in seeing.
While the demonstration is being organised, utilise the time to look at things like the vendor standard contract, pricing structure, what other costs may be involved, the financial viability of the vendors etc. All of these will come into the final decision, so you might as well get the review done while the project is awaiting the demonstration.
Usually when the package is reviewed, you will find each solution will have some impact on the project. The impact may be on business processes, implementation, customisation, training or a myriad of other aspects. After reviewing the packages, make sure to look at the impacts of each solution.
By the end of this phase we should be looking at one or at most, two packages. If you can see that one package is easily beating the opposition, you can reduce the effort in evaluation packages you know will not succeed, and become more focused on the one you can see will be successful.