What should I consider when deciding whether to delay an exam? I believe I may have scheduled an exam too early, and I am considering delaying it by a day or two. The material that I would cover fits in fairly well with the earlier material, and not as well with the later material. I can cover the material as is, but barely so, and the students would not have time to digest it or gain experience via a homework set. I have already put the approximate dates of our four exams in the “tentative” course schedule. 

What factors should I consider when making this decision, and how should I weigh these factors? 

Here are some factors I've thought of: 


Whether or not I have time to cover the material in class
How much advance notice is given (Changing the date the day before is probably too late, right?) 
Whether or not the students would like the exam to be delayed (I'm guessing they will!)
Department or institutional policies
Whether or not student accommodation services (e.g. make-ups, proctors, alternative formats, etc.) need to be scheduled in advance


Update

I think there are a few things that are clear (some from the comments—thanks!):


It matters whether or not any posted exam dates are described as tentative or firm. Tentative dates are estimates and students should understand that they are subject to change, whereas students may plan around firm dates. 
Exams should not be moved to a significantly earlier date. This is not fair to students. 
Students should not be tested on material they haven't had a chance to engage with (in and/or out of the classroom) or ask questions about. 
Special understanding and grace should be extended to students who miss an exam date due to a scheduled change (especially for short-notice changes). Of course, students who miss an exam for a school-approved reason (e.g. sports/research/bereavement travel) usually have the right to make it up anyway.  
If the instructor polls the students offering to make a change to the exam content and/or date, and they unanimously support the proposed change, then there's no reason not to do so. 


Epilogue

I polled the students before asking this question. Almost 60% of students preferred moving the exam date back one day to cover the extra material, and about 35% preferred keeping the exam on the same day but having it cover less material. In spite of their preference to delay the exam, and in spite of the dropped material fitting better with the this exam than with the next exam, I decided to move 25% of the content of this exam to the next exam. Thanks to all for the discussion!
Exam dates announced at the beginning of the semester should only be changed with a highly compelling reason. The syllabus of a course is a contract with the students. Even if 90% of your students prefer the delay, if one of your students has to cancel an airplane ticket for a conference visit or miss a wedding, a balance has not been struck. 

If I were a student in which an instructor tried to change an exam date as late as "the day before", I would certainly lodge formal complaints with the department and the institution. Please do not do this. 

In your initial post, you'd not given any reason to believe that you couldn't simply move a bit of material to the next exam. That is by far the better option. 

If for some reason delaying the exam is truly unavoidable, you should feel obligated to offer make-up exam times for students who may be unable to attend.