Did the Jews of the New Testament era think the time was imminent for the coming Messiah?

As Christians, we can look at New Testament passages and conclude the Jews of the New Testament era _were_ expecting the Messiah. What I am looking for in this question is: What evidence is there _outside_ the New Testament that the Jews of the NT era were expecting "very soon" the coming of the Messiah. And what understanding did they have of the type of person the Messiah would be and of the type of work he would accomplish? Did the Jews think the Messiah was coming _soon_ and _what type of work_ did they think would he do? Please show your sources. Thanks.