Mapping Center Answer:

I recently wrote a blog entry on how to create a large format display from an online basemap -- here is the link -- it might help:

Printing wall maps from the community basemap

One idea is to set up a display of your area of interest that has the amount of detail you want in the basemap, then export that map display as an georeferenced image (e.g., GeoTIFF).  Then you could insert a new data frame, add the georeferenced image (this will now be a static display), and then add your symbolized layers on top of that.  Then when you export the map, your layer symbology will be correct and the detail in the basemap will be right.

If you want a basemap with less detail, you will create your georeferenced image from a smaller scale; if you want more detail in your basemap, you'll use a larger map scale.  In either case, you just need to make sure that your area of interest is within the extent of the map image that you export.