Treaties don't actually bind governments all that much. Generally, there is pressure to sign them and not leave, but many governments agree to do things behind the scenes without formally signing a treaty.
Whether to sign up to the TPP is NZ's decision, but agreeing to it cedes power beyond just copyright, so withdrawing from it later is harder.
If NZ were to withdraw from the Berne Convention now, they would only suffer from the consequences in the realm of copyright. TPP appears to bundle several disparate things together, so there is serious leverage for others to prevent withdrawal if the treaty turns out to be significantly disadvantageous to NZ.
Pretty sure that was already done when NZ signed Berne in 1928 and TRIPS in 1995, both of which impose a minimum duration of copyright terms.