Just a quick question about the main character's quest for the g.e.c.k. I thought it was cool that the healer guy came to you in dreams at first, but it seems like if you aren't completely committed to the main quest your popularity declines with Arroyo. So I was wondering, is there a time limit before the game "ends"? Or, does your popularity decrease?

Im wondering this also

I don't think taking your time with the main quest has any impact on your standing in Arroyo. That said, after you're done with Arroyo's tutorial temple and basic sidequests, there's really no reason to ever return there without a GECK.
There is a time limit in the game, but it's extremely long; I believe that you have thirteen in-game years in which to complete the main plot and do all the sidequests you wish.