Caveat: I've been out of the ACGME game for over a year so anything I write you should double check.
There are caps, and from what I remember the caps are the same as Internal Medicine which I believe is 12 a day.
This site may help you.
http://www.acgme.org/acwebsite/rrc_400/400_prindex.asp
I remember that being odd becuase psychiatry patients often times require less maintenance than regular patients. In IM we had a cap of 12, and we had to cover the floor. Covering the floor took about 5-6 hrs a day, leaving with only a few hours to see your usual 7-12 patients. In psychiatry, covering the floor (responding to beeps and concerns that didn't have to do with the patients that were specifically yours) was less than 1/2 an hour a day on most days.
The stress of being beeped in IM even while seeing your patients was enormous. I remember being beeped on something of the order of 30x a day in IM. It was like have a bomb strapped on my back. At any moment it could go off. You rarely get beeped in psychiatry (at least at our place) because you're on the unit most of the time, and 1/2 of the patients you cover, while the other half the other resident covers.
However despite that cap, if we occasionally went over 12 (which when I was at the program was rare-happened maybe once 2-3 days a month), I didn't really mind covering, reason being is that if you look at the maximum cap, yes there's 12 pts max, but they could make you work 80 hrs a week too in addition to doing a lot of other things that could've been uncomfortable. The program never did that. We often times got out in less than 40 (minus calls). For that reason, I didn't decide to fire back because that can lead to the trap of a trench warfare mentality against people who are your superiors. (The juice has to be worth the squeeze).
I did mind other things. E.g. we had a time where one of the attendings just showed up, signed his stuff, and left--which put him on the unit for only about 1 hr a day. If you called him up, he didn't call back sometimes for 1/2 an hour, and when he was on the line you could barely hear him because his cell phone carrier blew. If the resident didn't know what to do, and it was an acute situation--SOTL, and the staff would try to blame the situation on the resident. That from my understanding violated his contractual and legal responsibilities with covering a unit. Blaming a resident when there should've been an attending present to handle the situation a resident can't handle? That was over the line. I was chief then, I felt I had to bring it up, and the then new dept chair fixed the problem.
So with the situation where a resident had over 12, and the attending wasn't there---that added the straw to the camel's back. I was not enforcing the cap which is fine by me so long as everything else was cool, but everything else wasn't cool. The guy wasn't doing his bare minimum responsibilities.
Any resident should be aware of the ACGME guidelines because they detail several of your rights and responsibilities as a resident.