Implications for the candidate if a contacted external evaluator declines
Chairs / deans / provosts will tell you that declining will have no effect. This is the official and morally as well as legally correct answer. 

However, I've had the great pleasure (not) of serving on a committee (at a private, elite R1) where the promotion review chair did not like the candidate and raised the issue that there were a certain percentage of declines to strengthen their tenuous case against the scholar ("no one likes/respects this scholar thus they are declining to serve as reviewers). 

This was counter to policy and in my mind immoral and possibly illegal depending on the circumstances. 

If you do decline, please include a phrase that you are declining due to personal / workload reasons and that the committee must absolutely not use your declination to in anyway prejudice the candidate's case. 



Now as to your subsidiary question as to whether you should feel obliged to write, this is more of a moral question. As a tenured full professor, I do feel an obligation to my discipline to do these reviews.

However, I will only do a review if I can do it well. If a candidate's work is out of my field of expertise or if my workload prevents me from doing a good job, I won't write. My first obligation is, after all, to my research agenda and my students. 

Furthermore, there have been cases where I know too much about a candidate to write an objective review. In those cases, I ask to be relieved due to a conflict of interest. 

There are varying opinions on whether one should write negative letters and this should really be a separate question. My own philosophy is that my letter is a third-person's neutral observation of the strength of the candidate's application for tenure. I thus write about the strengths that I see for this case, but whether the strengths are sufficient for tenure is ultimately a decision that should be made by the tenuring committees.