There are two similar expressions: (1) "the straw which broke the camel's back" and (2) "the last straw". The choice of subject, verb and verb tense depends on context and intended meaning. However, in both cases, "it was" or "that was" is very common. The past simple is usually most appropriate because the placing of the straw on the camel's back or the appearance of the last straw normally happens at an instant in the past and so they are completed events with no repercussions in the present.