in all honesty, I had more free time in college than any point in my life since. In comparison, college is the easiest time of your life; in that sense, it is definitely possible.
In short:
In a typical college environment with an exotic animal, everyone who sees it wants to play with it. YOU CANT LET EVERYONE CROWD AND PLAY WITH YOUR CHAMELEON. This WILL stress it out.
I think it *GREATLY* should depend on your reptile experience. If you have no other reptiles, I would STRONGLY SUGGEST AGAINST a chameleon. You CANT play with them all the time, they are very expensive, etc etc you've heard it. If you have reptile experience, then I don't think a chameleon is very hard to keep at all in a college environment. HOWEVER, if you do NOT have reptile expeirence or you want an animal that you can "play with" and "show and tell" I would lean you towards Colubrids (non-venomous small snakes such as ratsnakes, kingsnakes, cornsnakes, milksnakes). They are harmless, good with being handled, and very very easy to care for. There are several other species that are more suited for the "ooh and aah" factor that comes with owning one in a college environment.
Given they generally want to be left alone, you don't have to "babysit" them very much. The persistant dedication is in understanding their caring and habitats (which is mostly time spent reading) and then once you have a proper habitat it is simply keeping a sharp eye on your animal and monitoring it closely.
Instead of feeding it a random cricket whenever you feel like it, make a log of when and how many you have fed it each day. This way over time you can track its eating habits. Similar for shedding, etc.
These things obviously take a few extra seconds, but if you have just 1 panther, the time required to take care of him isn't immense. Hand-misting (assuming on a college budget you dont have a misting system) takes a minute a few times a day; overall I doubt you would spend more than 15minutes/day attending to his care.
DO CONSIDER THE TIME REQUIRED FOR THE FEEDERS. Are you going to buy new crickets every week? Are you going to culture them yourself? Both of these have additional time and money requirements. Don't forget that you also have to dust your crickets (and ideally gutload them) so this is all added time, depending on how well you truly want to take care of your chameleon (IMO, you should consider all these things "required").
Also, do consider ALL COSTS. Just to give you an example, I am currently designing and building my own 2-level enclosure for my kingsnake and ambilobe (actually getting him tonight so excited!). NOT counting the cost of the enclosure itself, nor any plants nor animals, I have already spent over $500 on reptile equipment. Granted, I am going "all out" with a full misting system, separate day/night cycle bulbs, multiple timers, and multiple T8 bulbs along with live plants and the like. But the "basics" will still run several hundred dollars easy, and you will need to spend at least another $20-30 on a UVB bulb every 6 months. Plus, depending on whether or not you have other reptiles you may need to buy some equipment (critter keeper for your crickets, timers, etc). There are also the regular supplements that you have to purchase.