I have been doing freelance graphic and web design full-time for over 25 years for over 150 corporations and small businesses. I honestly cannot remember the last time anyone called me and did not use the term "rush" or "emergency"! In actuality I have one seen "one" graphic "emergency" in all those years. I have had several corporate clients email me or call me as little as 4 hours after assigning an 8-12 hour project asking me if it was done!
It is amazing how people (clients) have changed over time. When I first started computer design work in 1989, very few people even had computers (and all I had was a Mac SE with a 9" B&W screen). A 300dpi scanner was $10,000! The local printers where I lived could not even accept a digital file. Color Management was all but nonexistent. When people hired me, there was very little competition and no frame of reference. As time progressed, "email" was the first wrench to be thrown into the system - now clients could start firing off emails asking project status, making revisions, etc. and all those emails had to be answered (sometimes taking longer to compose than the actual projects) - today that is even worse - I have had some 4-hour logo projects that required over 100 emails back and forth to clients that simply will not pick up the phone! Texting is out of control! There were no "rush" jobs back then as nearly every print project required sending off a disk to a printer and having plates burned and then having a $300 color match print mailed back for client sign off - for every page - if there was a color or other problem the whole process would start over. So getting in a hurry just did not happen.
Then came the invention of PDF and the "free" reader app. Now every client was conned into believing that they could proof color accurately on their entry level monitor with no color management. That led to years of explanations to clients that what they were seeing was not accurate (another time suck) - that still continues.
About that same time the Fed-Ex Overnight phenomenon was born, and instantly people became nervous wrecks and the most mundane print project had to be received the next day or the world would end! I had one major client that spent over $250,000 with me in 2004 and $120,000 of that was FedEx reimbursements to me (not an uncommon ratio). In almost every case, if I went to their local office, I would see overnight shipments I made to them still sealed up in the boxes unopened weeks after receipt. People will sometimes haggle over design/printing prices, but will spend ANYTHING to ship it overnight!
Then came the invention of the Mobile Phone (just when you thought it could not get worse). Clients now try to color proof my designs on a postage-stamp-size screen while driving down the freeway at 70mph! "Could you make that teal a bit more green?" to which I would respond, it is "blue"! God forbid if you ever have to get in a corporate meeting with that circle of dim-bulbs - nothing like driving across town and sitting around a table with six people that don't look up from their little phones for 45 minutes and spend the whole time responding to text messages and tweets! I have not been to a single corporate meeting in years where a single thing gets decided of any consequence, but they are all on salary and all they do is have meetings to make it look like they did something that day.
Then the creme-de-la-creme, the advent of Social Media. Now I no longer design for "a client" - no matter what I design 9 times out of 10 the client has posted it to Facebook for the whole world to make comments and suggestions. If just one anonymous person makes a comment, the client has a full on fit! Most clients place more stock in what some unqualified stranger says than the professional they hired! This is now true of everything today - few people are left that can actually make a decision on their own, so design really drags out (and most designs usually get worse as they look like they are designed by committee before it is all said and done).
So such is the life of a digital freelancer today. I just assume that everything is a rush from the outset and charge accordingly, knowing full well that the actual "design" work will take less time than the emails, phone calls, overnight shipments, revisions over time they log in another opinion, etc. One thing I have learned for sure - after a lifetime of taking and teaching countless seminars of concepts such as Color Theory - save yourself some time and effort and just have your client go ahead and ask his wife what her favorite color is from her sorority days, because that is the color(s) you will end up using regardless of how many VP's are involved!
If you can get hired as a true "designer" on a retainer basis where you have the final say, then that is great, but most people looking for a Freelancer today where they can rent a few hours don't usually just accept your first (or best) design. I have also noticed the past couple years another new wrinkle in that more and more clients have purchased subscriptions to the Adobe Creative Suite, most of whom have no idea how to actually use any of the apps. So they are trying to hire me to create work to their specifications and demand my native files so that they can learn how I do what I do which opens up a whole new can of worms. Therefore, I have been turning down more and more of those jobs.