Well to answer that I would need some context. Like :
a) Do I need the cash and is the market quiet at the time?
b) Are there some other opportunities that might result?
c) Is the hourly rate way higher than I could get somewhere else?
d) Is the tedium only short term?
e) Am I gaining some significant skills / experience?
f) Did I give my word to do the job?
If the answer to any of the above is yes, I may well accept the project or continue on with the project, otherwise I would move on.
I remember when I was working in London, I was on the same contract for 2 years. About 9 months out from the end they extended my contract and we were asked to build a prototype of a system that automated a lot of human elements of the original system we built. We built the prototype, and it was very good, but the funding was pulled and most people left the project. By that stage I was about 4 months from my visa running out, and there was no work to do. So I stayed on and did nothing but about 30 minutes of support work per day and the rest of the time worked on pet projects and amused myself. I felt a little bad about it, as I was earning $120/hr, but I may well have been screwed if I tried to find work with only a few months left on my visa.