I'd jump at the chance of becoming a TA, although at my uni they don't allow anyone doing an undergrad or masters course to do it (i.e. - only PhD students can do it).
Anyway, what I'd do in your situation is find out when my dissertation/research project (whatever you may call it) is due to be all written up and handed in. In my experience (I'm a masters student at the moment), I found the time when I was doing my research project painfully time-consuming, since I had it and classes to juggle. My research took up the entire first semester and was to be written up for the end of January, and after then I had A LOT more free time. I dunno if you can start the TA position any time you want, but if so, I'd definitely avoid doing it at the busy time of the year.
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