How to gracefully walk away from coauthored paper I am working on a coauthored paper which I would like to step away from. How can I do so very tactfully and gracefully? 

I want to step away because I don't quite agree with the direction the paper is taking in terms of analysis; the publication prospects are not terrific; and, frankly, I am not sure if I fully believe the results (our setting is not very "clean," meaning that there are several alternative explanations). I don't necessarily want to say all of these things to them.

Another detail is that the coauthors are two people at my current institution. I am going to be transitioning to another institution (in another state) in the next few months. Note this is not one of my main reasons to walk away, but being away will make it somewhat harder to collaborate. It will also be nice to get this off my plate so I can focus more on other projects.
This is more a warning of the consequences than a real answer. There may not, in fact, be a way to do this gracefully. 

You need to decide what the paper will become without you. Technically, they can't publish it without your permission. If you aren't a co-author, will you want acknowledgement? Will you want your name listed at all? 

If you don't want your name listed and you have contributed to it, then publishing it could open the others to a plagiarism charge. 

So, the situation is a bit sticky. If the paper can't be published without you, then there could be hard feelings and sometimes such things are a bit "sticky". 

I suggest that you need to work out the details with them, to just withdraw. You may have some leverage to improve the paper and stay on the list of authors. But you might need to take some responsibility for the project to accomplish this.