I have put quite a few of our larger tubs on wooden decks with good results.
If your deck is built to standard floor specs, it should hold the tub just fine, but it will most likely sag over a period of years. What to look for: joists on 16 inch centers, not 24 inch centers, and that the span of the joists doesn't exceed standard building practices: that is, about one foot per inch (a 2x8 spans less than 8 feet, a 2x10 less than 10 feet etc).
To keep from having trouble down the road, a couple of extra peir and post combinations can be added near the center of the tub - with a 4x4 or 4x6 beam between them. This can be a very simple addition if you can get under the deck - you will have to tear off a couple of deck boards and do it from the top if you can't get under.
If you just can't do the peir/post part because of limited access, you can simply double up a couple of the joists or a beam under the spa.
A final idea: if you can't get under your deck at all, and it has less than standard construction, you can build a new section of deck on top: going from existing post to post, but overbuilding. This can also be done by simply taking out the section of deck that will be under the spa and rebuilding just that section, keeping in mind that the tub will cover your work so it doesn't end up looking bad.