Graduate School Offer of Acceptance Due Dates in the US?
As noted by @NateEldredge in a comment, almost (and I only say "almost" because even one exception would preclude saying "all") every university in the US admitting students to a biomedical sciences PhD program does so based on the April 15 resolution:


  Students are under no obligation to respond to offers of financial support prior to April 15; earlier deadlines for acceptance of such offers violate the intent of this Resolution. In those instances in which a student accepts an offer before April 15 and subsequently desires to withdraw that acceptance, the student may submit in writing a resignation of the appointment at any time through April 15. However, an acceptance given or left in force after April 15 commits the student not to accept another offer without first obtaining a written release from the institution to which a commitment has been made. Similarly, an offer by an institution after April 15 is conditional on presentation by the student of the written release from any previously accepted offer. It is further agreed by the institutions and organizations subscribing to the above Resolution that a copy of this Resolution or a link to the URL should accompany every scholarship, fellowship, traineeship, and assistantship offer.


This means that you will not have to accept any offer prior to April 15th, and that no accepted offer is binding until after April 15th (though it would still be impolite to accept and then withdraw, so this should only be done in extreme circumstances). The explicit purpose of this resolution is to not allow universities to pressure students to accept an offer before other schools are done presenting their own offers.

Once you know for sure which offer you want to accept (and no earlier), however, it's good to accept as soon as possible and let other institutions know you will not be attending - this can let them extend offers to people on their waitlist and therefore gives those waitlisted applicants more choice.