When someone gives me a manuscript or other text to read and/or edit, I return it with comments as soon as I can, ideally within a few days, though the time depends on the length of the document and what other priorities and deadlines I have at the time. There are certainly times when I take longer than a few days to return comments, but in general, a document to edit (e.g. a thesis chapter, a manuscript draft, a proposal draft, an abstract) is a very high priority for me, whether or not I am a co-author or co-PI.
Experience has shown that this is just one of many strange things about me, and also a reason why I am not always a joy to work with. Most people take longer to return comments on a document, and, in a collaborative relationship, this can lead to mutual annoyance. I can get annoyed at the delays, and my colleagues can get annoyed at how hyper I am about making progress and finishing projects and manuscripts.
Most of my students appreciate the timely comments, but not all of them do. If a student gives me something to edit and I hand it back in a day or two, the response can range from "Thanks for the quick turnaround" to "Oh no, I don't want to see this again so soon".
My students sometimes ask me how they can get more timely comments from committee members or co-authors who are taking a long time to read and edit drafts and therefore delaying the student's progress towards manuscript submission (and possibly degree completion).
Here are some options:
1. Do nothing. Wait. You can do this (a) calmly or (b) not calmly.
2. Do a few things. Polite reminders by email, casual questions in the corridor or restroom (if relevant) etc.
3. Blackmail/threats of the "I'm going to break down completely and it will be your fault if you don't read my thesis draft soon" sort; or the "My dying grandmother's last wish is that I get my degree by December 7 of this year, so can you please get back to me soon with your comments?" sort.
4. Ask the grad advisor, department chair, or someone else to intervene in extreme cases.
In fact, I don't recommend some of the items in this list. The situation can be difficult for all concerned. Everyone is busy, and some people are so insanely busy with work and life that there's no way they can provide thoughtful comments even within the time frame of a few weeks. This happens to me as well during extremely busy times (e.g. before a proposal submission deadline when my husband is out of town and I am teaching a lot and I have an exam in my language class and my daughter has lots of after-school activities and my cat has laryngitis). Fortunately, life isn't like that 24/7/365 and it should be possible to read and comment on a draft, even a long thesis, if given sufficient time.
Polite, reasonably spaced reminder emails (or phone calls or in-person conversations) can help make sure that a document doesn't get lost in the crowded inbox of a busy person, though try not to cross the invisible moving boundary between polite reminding and obnoxious pestering. If you have a deadline, it is of course important that you provide the document for review well in advance if at all possible. And it's OK to remind people of the deadline once it starts to loom large.
If a situation really starts to drag out because someone doesn't have time to provide comments after they have had a document for a reasonable amount of time, extreme action must be taken. Note, however, that 'reasonable amount of time' is a flexible concept depending on the length, complexity, and importance of the document, and the personalities of the readers. Ideally, the 'reasonable amount of time' is something that has been agreed on by all concerned, or involves a deadline that has been announced well in advance.
If you need something (text, data, comments) and the other person is extraordinarily slow at providing these (despite having agreed to do so), there's not much you can do other than the occasional polite reminder/query, working on other things in the meantime, and trying various calming activities and substances so that you don't spend inordinate amounts of time being anxious and angry.
If you're a student and you need comments on your chapters/thesis, it's a good idea to talk to each person who has to read your thesis draft, and find out when they want the document -- e.g. how far in advance of when you absolutely need/want to be done. I like it when students ask me this. If the student is organized, has a plan, and gives me the thesis draft on the agreed-on date, I can plan ahead, knowing that I have to make time to read the thesis during a particular week or two. I consider 2 weeks a reasonable time frame for reading a typical thesis (whether or not major parts of it have been published already).
If a committee member (or even the advisor) can't keep to an agreed-on schedule and the situation gets dire despite repeated calm but urgent discussions, it's time to talk to the grad program advisor and work out a reasonable solution for everyone.
There are always going to be people who are slow to respond to request for comments on documents. It starts with committee members/advisors who are slow to provide comments on the thesis, and proceeds to reviewers who are slow to review manuscripts and editors who are slow to make decisions. If you do collaborative research, there will always be some colleagues who are slower and less responsive than you might prefer, and this can make you extremely anxious if you need to submit manuscripts for various important career reasons, not to mention communicating your amazing research results and ideas. That's why it's be good to do some research on calming activities; you'll need these throughout your career.
12 years ago