Hey David -
There is a Calendar date selector which appears when you choose the Anchor Date of a Relative Date Filter. The same calendar also appears when creating a Parameter of type Date. However, there is no Calendar picker related to Quick Filters...sorry.
There probably is already an "Idea" out there to add this to the product: Shawn Wallwork watches that stuff pretty closely and might be able to point you to it if it exists. Otherwise, you should request it as a feature!