Yes, sitting can be quite tricky, which probably sounds strange to someone who does not have hip problems! When I went to visit my mother in Sweden a few weeks ago, I discovered that all of her furniture was exactly the wrong sizes for me to sit on comfortably for any length of time. (Last year, neither hip had gotten to the stage that I noticed this!) Most of her furniture is much smaller than my own chairs and couches, and I just could not get my "unfixed" hip at a comfortable angle. My resurfaced hip was perfectly fine, but the other one hurt more than ever and almost ruined my vacation. Believe it or not, even sitting on an airplane for about 12 hours on the way home was better!
I agree with Dan that it helps if you can move the hip around every so often. I get very stiff and sore if I sit in the same position for very long. Also, my recliner helps a lot, because I can support the leg at various angles. My bad hip got better almost immediately once I got home.
I don't think you'll have to worry about it after the surgery, except perhaps for a week or two - especially if you have a recliner or a comfortable couch that can provide support for your leg at various angles.