There are two Biblical arguments for when Jesus was born. Ironically, neither land anywhere near the month of December or even close to the birthday of Tammuz, December 25th. These are the two best possibilities of when Jesus was born.
1) Passover Week
This belief is based upon Luke 2:42 which says: “And when he [Jesus] was twelve years old, they went up to Jerusalem after the custom of the feast.” In the Greek, this verse reads: “And when he was becoming [ginomai, prolonged tense, middle voice form] twelve years old, …”.
Some believe this means Jesus was becoming twelve years old during the very week of the feast. If so, this would make the birth of Jesus close to the very time that he died which in my mind seems to disagree with what most scholars say (i.e. Jesus died at 33.5 years of age). Therefore, my personal conjecture on the birth time of Christ is the Feast of Tabernacles which would answer this question and numerous other questions. Also, the Feast of the Tabernacles was a feast which remembered how the Israelites sojourned through the Wilderness of Sin (Sinai wilderness) in tents for forty years. Ironically, if this is the proper time frame for Jesus’ birth, then it could serve as a picture of how Jesus sojourned through this wilderness of sin, known as earth, in the “tent” or flesh of mankind. The arguments included in the following link are very thorough in their analysis of Scripture. I hope you will enjoy the calculations and Biblical cross-referencing that this author does as much as I did.
Keep in mind that the feast of tabernacles was related to Israel dwelling in temporary booths during this holy festival to commemorate their dwelling in temporal booths as they traveled forty years through the Wilderness of Sin on their way from the slavery of Egypt to the Promised Land. The symbolism that one can pull from this historical event of Israel should be apparent. Promised Land for Christians is heaven. The Wilderness of Sin seems to reflect the sinful trek through this wilderness called Earth and Life. Egypt appears to mirror the old life before Christ ransomed Christians from bondage. All of this being said, we are all dwelling in temporary tents or booths known as earthly bodies as we travel through this life. Is this festival the day that Jesus chose to begin His journey through this Life on this Planet as He took upon Himself a human body?
Not only does the article at this link show very compelling evidence for this belief, but the pastor in the video at this link and this link also appears to believe that the Festival of Tabernacles is verified by the Scriptures. Personally, I am not adamant on the time of Jesus’ birth, but I firmly believe that this festival has the most convincing proof of any arguments, especially since the Scriptural arguments that are used seem very convincing.