Jeff - do the filters which appear on the Filter Shelf as a result of adding the quick filters have "Sigma/SUM" symbols next to them (this indicates that field being filtered is not used anywhere else in the viz)?
If so, you've created a "Calculation Filter". These puppies essentially must ask the cube to partition the data by the filter value (via a calculation), and THEN display the result. I'm not an Essbase user myself, but I see the same behavior you describe against SQL Analysis Services. It's an expensive process for the cube to deal with, for sure.
The solution? Don't do that
Seriously, though: I'd try to re-work the viz a bit so that the field you're going to filter is already used by the viz -- see if you can get it on rows/columns/level of detail without things getting distracting. Once the field is part of the viz, it's no longer necessary to do the "expensive calc"
Hope this helps!
Thanks for the effort, but the filter is not based on a calculation. There is not sigma symbol. The filter is of a date hierarchy Year\Week. We have 11 years with 52 weeks per year worth of data in this cube. When the filter is added the default behavior is to be multi-select and shows the hierarchy header. This allows the user to click on the second (more granular detail, weeks) hierarchy header, represented by a (1). When they do this Tableau selects ALL of the weeks for 11 years to create a filter on. This operation will consume roughly 8gb of memory, be time consuming, and may not return at all. Total freeze.