Actually, INS was split into 3 agencies...
CIS: Mostly clerical, handling naturalizations, LPR's, asylee claims, refugee claims, etc.
CBP: Officers and Border Patrol Agents, Ports of Entry and gaps in between, respectively. Also covers the Air and Marine units.
ICE: Criminal Investigators, Deportee Officers, Enforcement Agents. These are the guys that break down doors and whatnot. Remember, they handle not only Immigrant matters, but also anything importable (ie, Customs matters), they're also big into investigating child porn cases.
Now remember, if you say you wanna see them doing their job, then don't blame the individual officers. CBP Officers and Border Patrol Agents really really wanna do what they're suppose to. By this, I mean send people back to Mexico or Canada. If you want a finger to point, please blame upper management and the politicians. They come up with the shittiest regulations on how we do our job. Years ago, if we didn't want someone to come into the country, we'd say, you're not coming in, turn them around, and send them packing. Process took maybe 1 minute. Now I have to do 2 hours of paperwork plus to kick someone out.
Mind you, I still enjoy doing it. I could just do a lot more of it if I didn't have to do the damn paperwork.
To put this in perspective. I live in Western NY. There is a heavy hispanic population of migrant workers. When coming home from work, its probably a good idea to keep the gun on when you go to the bank, especially on fridays. I get way to many stares when I walk in with my uniform on.