I recommend a polite e-mail response with a statement along the lines that you understood that the universal reply date to accept/decline offers of admission and financial support was April 15, as per the Council of Graduate School's April 15 Resolution Regarding Graduate Scholars, Fellows, Trainees, and Assistants ( http://www.cgsnet.org/april-15-resolution
). And, that while you understand the importance of deciding as quickly as possible, you will need time to visit other schools and to consider your options.
These "early response" requests happen every year (and not just in the context of graduate admissions). As has been noted in other threads, graduate applications are reviewed by faculty and the offer letters and e-mails are not always vetted by the administration to verify that they are factually or legally correct. For example, a new faculty member may not be aware of the April 15 resolution if they were not educated in the US, or an older faculty member may have simply forgotten about this resolution since it has been so long since they were involved in the admissions process.
If you continue to get push-back regarding an early decision date, I recommend (1) take this into consideration when making your decision (do you really want to be affiliated with a program that cannot correct its errors?) and (2) notify the Graduate School of that University that one of their departments is not abiding by the April 15 resolution. However, I also should clarify that the April 15th resolution is for graduate schools, not for medical schools, and interdisciplinary programs such as medical physics are sometimes located in the medical school, not the graduate school, so folks in medical physics do sometimes have an earlier reply date than the rest of us.
Finally, even as I abhor hearing of schools playing hardball tactics to get early responses, I do still urge everyone to let departments know as soon as possible if you have decided not to attend (even if you have not made your final decision yet). Although most schools can estimate the percentage of students who will accept their offer, the earlier we can know that we are under (or over) our target class size, the sooner we can let those on the wait list know their fate.