I want to know if I should use deoderant and take fewer showers from a
water consumption standpoint. Or does the production of a stick of
deoderant -- including all of the chemicals, packaging and
transportation -- take more water than I would use taking two showers
a day?

Assumptions:
Stick of deoderant lasts about 1 month 
5 min. shower uses 12.5 gallons 
65 showers per month w/no deoderant = 812.5 gallons
30 showers per month w/deoderant = 375 gallons
difference = 437.5

I realize it's unlikely that it takes several hundred gallons of water
to make a stick of deoderant. So the answer I'm looking for is strong
and authoritative numbers telling me how much water is used to make
something like a stick of deoderant.

Wanna save water? Choke down that shower head to a gallon a minute or
so, for starters. Install a high efficiency head with a shutoff and
turn off the water when you don't actually need it.

What's up with you that you need 2 showers per day?

Well, first, there are alternatives to stick deoderant:
http://www.vegansociety.com/catalog/product_reviews_info.php?products_id=202&reviews_id=34
http://www.crystaldeodorant.com/business/index.html

Second, as Mark mentions, there are shower heads that reduce water usage.
http://doityourself.com/shop/watersaverchromewall.htm