Sources are legion on any search engine.
http://www.jcstudies.com/articleDetail.cfm?articleId=59
Jesus And The Holy Tongue
Author: Dwight A. Pryor
DID THE HISTORICAL JESUS SPEAK HEBREW? The supposition of New Testament scholars—indeed the virtually unchallenged assumption in Bible dictionaries and Gospel commentaries for well over a century—is that the native tongue of Jesus was Aramaic, not Hebrew.
That is beginning to change. The cumulative research of a generation of scholars living in the land of Israel, both Jews and Christians, strongly challenges this conventional conviction as outmoded and misleading...
...First, with the resurgent nationalism evoked by the successful Maccabean revolt a century and a half before Jesus, came a corresponding revival in Hebrew as the national language of the Jewish people. Second, the discovery of the Dead Sea Scrolls has confirmed that by the first century Hebrew was again a spoken language in Israel. The various documents, the vast majority of which are written in Hebrew, reflect a distinctive and developing Hebrew language in spoken as well as written forms...
You have a similar situation today with koine Greek, the language of the New Testament, which is still the liturgical language of the Greek Orthodox Church, and the Slavonic of the Russian and other Slavic Orthodox Churches, which was devised for Slavonic liturgy in the 9th century.
neither is spoken, but used in the religious environment and, just as Hebrew is related to Aramaic or vice versa, the same can be said of the other two. But no one really speaks them conversationally.
In America, most Jews don't speak Hebrew at home (specially not biblical Hebrew), but read Hebrew scriptures in Hebrew. The author also uses the example of the Essenes as proof that Hebrew was a spoken language. Essenes were a small sect which did not represent the general population of Palestine, and there are no documents that show the degree to which this may or may not be true.
Obviously Hebrew was not dead, at least liturgically, but we don;t know how much it was in use. Again, it is impossible to check up on the sources your article claims if they are not mentioned by name.
Your author also mentions Hebraisms in the NT but doesn't give any listing of them. But he neglects to mention numerous Aramaic words, names and references, such as Hosanna, Korbun, Mammon, Maranatha, Thomas, Cephas, Eli, Gethsemane, Golgotha, Akeldama, Abba, etc.
At any rate, the point of my mentioning Aramaic in reference to john 3;3 is that the pun the author of John is trying to portray is possible only in Greek (and that is even a stretch), and not in either Aramaic or Hebrew, which means that Jesus would be speaking sophisticated Greek to a member of Sanhedrin, which is, to put it mildly, a very unlikely and unusual gesture.