The Dead Sea Scrolls and Jesus' first language

I'm currently reading Who Wrote The Dead Sea Scrolls?: The Search For The Secret Of Qumran by Norman Golb. If you haven't thought about the scrolls recently, I commend this book to you: this book changed mine.

A brief thought this morning. Golb (in evaluating the importance of the scrolls) speaks about them as indicating that Hebrew had become a far more prevalent language throughout Palestine in the first century AD, as a consequence of the territorial expansion of the Hasmonean kingdom.

I'm intrigued by this thought. I'd always been taught -- and assumed -- that Jesus probably spoke Aramaic as a first language. Golb has made wonder otherwise. The 2 proofs given that come to mind are Mark 5.41 ("Talitha cumi") which is usually described as Aramaic, and Jesus' use of "Abba" as a term of address. However, my first source I read today indicates that "Talitha cumi" could be either Syriac or Aramaic, and Abba either Syriac or Chaldee. Since Jesus grew up in Nazareth, I wonder if Syriac might have been a household language in that area. (It shouldn't be assumed that a child in northern Palestine might not have grown up speaking more than one language in day to day life).

(Those of us living in the US don't know how lucky we are sometimes, language-wise. In Palestine, I suspect there was the language of the home, then Hebrew for synagogue, Greek for commerce, and Latin for dealing with Roman officials. Whew. I have enough trouble dealing with English, and occasional Spanish, and an even rarer use of my few words of Mandarin or Thai).