The problem is not the 4x4 posts, its the (southern pine?) 2x8s. Assuming that you intend each 2x8 as simple 8 feet spans, they (the 2x8s) are overloaded in both shear & moment. To answer your specific question, I compute that you need 19 each 4x4 posts.  Each interior 8 foot long 2x8 would need it's own post at each end and at midspan. The exterior 2x8s have about half the load of the interior members, and would need a post at both ends. You specified 16 inches o/c, so 7 each (2 exterior + 5 interior) 2x8s are required (6 spaces at 16 in each = the 8 foot width).

If you can consider members larger that 2x8s you should be able to do what you want with a reasonable number of posts.

A rather rambling response but hope it helps. Make sure you check the local buildings codes.

I've built quite few decks with treated SYP and have always used 2x6's for the framing, no long spans. The layout I use is 4x4's on 5' centers with girders of (2) 2x6's, one on either side of the 4x4 and through bolted with HDG ½" fasteners with 2" square washers.  The floor joists are laid perpendicular to the girder on 16" centers.  I have used both nails and brackets to attach the joists.  I have also used 4x4 blocking to attach the joist to the girder when using a Pau Lope or other exotic wood.   
Treated SYP usually has a very high moisture content and the shrinkage is very high, up to a ½" on the width of a 6x5/4 board.  So if you can purchase your lumber and rack it to allow it to dry out.  There is another treated SYP material that does not have CCA, though I hear it has the same moisture problem.  Always use the wood treated for ground contact (45), which is usually available from the big home improvement stores.  This is especially true around the Hot Tube. With face screws (S/S) we usually make the deck boards tight due to the shrinkage.  There are several hidden fastener systems that you should look at, EB-TY, Deckmaster Strips, Deckclips.  Face screws (S/S) and nails (S/S) will work out eventually.

Use HDG Nails or Bolts, the uglier the better.  If possible use S/S Nails and Scews. Do not use mechanically galvanized fasteners.
Make sure crown up on all borads..
If you use screws use the #17 point screw or you may have to predrill.
Use square drive screws. Keep several bits on hand.    

http://www.stainless-fasteners.com/commons.htm

www.mcfeeleys.com

www.trimscrew.com

http://www.ebty.com/home.htm

http://www.deckingclipenterprises.com/

http://www.diamonddecking.com/

SlideRule...
I am not tied to any specific size joists.  I have plenty of room to be flexible.  What would be the best way to accomplish what I need to do short of pooring a concrete pad and dropping the tub all the way down to the ground?

tctim - For the size (8' x 8'), loading (150 PSF), height (3'6"), and embedment (44" in concrete) that you specified the following combination of treated southern pine members (#2 or better) should be adequate:
1. 2x10 stingers, 16 in. o/c, 8' long (max)
2. Double 2x10 headers, 8' long (max)
3. Four (4) each 4x4 posts, supporting each of the two (2) double 2x10 headers. Posts approximately equally spaced.
4. Suggest that you consider 2x6 or 2x4 decking instead of 1x4.

Also please consider retaining a local structural engineer to detail the connections of the members based on your specific situation. Typically this is more critical for heavy loading applications, such as yours, than sizing the members themselves.