Yep, it is almost essential to have everyones involvement! In fact, we had several residents that encouraged fluids as well...and that helped with the whole "yeah yeah right...nurses always say that" attitude.
I found that if I put a nice pitcher of water with a little ice and have dietary bring lemon wedges that people drank more water! Also, I found some people really liked the flavored water or sparkling waters! Checking if it needs to be refreshed is also great...reminds them that it is there for them at any time (and making it within reach...for those that can pour and drink on their own...if they can't then frequent checks and help is needed).
Using other words than water is also helpful! For me...well I really got sparkling water popular, so I would ask if they would like their sparkling lemon drink or something along that lines...makes it more tantlizing to the senses and a bit more desirable!
ALSO, why use a clear cup? That can be boring. Studies have shown that if you use color in both food presentation and fluid presentation the more desirable it is (again feeding more than one sence!). I use colored cups when available, or a colorful straw (if it can be used by the res.). This is also a great trick for people that don't eat as much as they should (even if you just do a colorful placemat...studies show an increase in consumption with a colorful placemat alone!