There is a really odd part in Luke in which Jesus’ rise is detailed. He begins preaching in a synagogue. The people are at once amazed, and they wonder: “Is not this Joseph’s son?” (Luk 4:22). Jesus then responds to this murmur:

Luk 4:23 And he said unto them, Ye will surely say unto me this proverb, Physician, heal thyself: whatsoever we have heard done in Capernaum, do also here in thy country.
Luk 4:24 And he said, Verily I say unto you, No prophet is accepted in his own country.
Luk 4:25 But I tell you of a truth, many widows were in Israel in the days of Elias, when the heaven was shut up three years and six months, when great famine was throughout all the land;
Luk 4:26 But unto none of them was Elias sent, save unto Sarepta, a city of Sidon, unto a woman that was a widow.
Luk 4:27 And many lepers were in Israel in the time of Eliseus the prophet; and none of them was cleansed, saving Naaman the Syrian.
Luk 4:28 And all they in the synagogue, when they heard these things, were filled with wrath,
Luk 4:29 And rose up, and thrust him out of the city, and led him unto the brow of the hill whereon their city was built, that they might cast him down headlong.
Luk 4:30 But he passing through the midst of them went his way,

When it comes to odd things to become enraged over, this seems to take the cake. Verse 23 indicates that Jesus is telling the people of Nazareth he will start doing miracles in the future, the people will see them, and he will deny the miracles to the people of Nazareth. It could be that the people are angry over Jesus’ prediction of future miracles or the unflattering predictions of their own actions.

Probably, the real reason the people rose up against Jesus was that he used an example of a prophet going to a Gentile over the Jews. He was, in effect, saying they were worst than Gentiles. See 2 Kings 5 for the account of Naaman.

Albert Barnes cites one possible reason of the anger as such:

5th. That it was a part of his design to preach the gospel to the Gentiles, and not confine his labours to them only.

This possible reason is re-enforced by the extra-Biblical claim of Josephus:

Now there was about this time Jesus, a wise man, if it be lawful to call him a man; for he was a doer of wonderful works, a teacher of such men as receive the truth with pleasure. He drew over to him both many of the Jews and many of the Gentiles.

Contrary evidence in favor of Jesus being sent only to the Jews can be found throughout the Gospels: In Mat 15, there occurs the most pronounced incident:

Mat 15:22 And, behold, a woman of Canaan came out of the same coasts, and cried unto him, saying, Have mercy on me, O Lord, thou Son of David; my daughter is grievously vexed with a devil.

If a modern Christian were to guess at Jesus’ next actions, it would probably be the exact opposite of what actually occurred:

Mat 15:23 But he answered her not a word. And his disciples came and besought him, saying, Send her away; for she crieth after us.

The disciples are trying to send this Gentile away, and Jesus takes to ignoring her. What is going on in this situation? Is Christ being un-Christ-like? Finally, after enough pestering Jesus rebukes her:

Mat 15:24 But he answered and said, I am not sent but unto the lost sheep of the house of Israel.
Mat 15:25 Then came she and worshipped him, saying, Lord, help me.

After the rebuke, the woman, graciously, begins to worship Jesus. If the modern Christian would be inclined to guess again at Jesus’ next action, they would again be dead wrong:

Mat 15:26 But he answered and said, It is not meet to take the children’s bread, and to cast it to dogs.

Instead of helping this woman who is worshiping him, he calls her a dog. Jews thought of the Gentiles as unwashed heathen, not worthy of their time, thus, the potency of the parable of the good Samaritan. The woman persists:

Mat 15:27 And she said, Truth, Lord: yet the dogs eat of the crumbs which fall from their masters’ table.
Mat 15:28 Then Jesus answered and said unto her, O woman, great is thy faith: be it unto thee even as thou wilt. And her daughter was made whole from that very hour.

This is an interesting passage from which Christians can learn much. A sinless Jesus was calling names and refusing to help someone in need. His priorities were elsewhere (the Jews). If Jesus was systematically ignoring Gentiles like this, how many Gentile followers did he actually have? And note that Jesus explicitly says his ministry was only to the “lost sheep of Israel”.

Another story of Jesus’ interaction with Gentiles can be found in Luk 7, in which a Centurion uses Jewish elders to communicate to Jesus for help. The text explicitly points out this Centurion helped out the Jews in the past as to set up a Quid Pro Quo situation.

Other evidence that Jesus’ ministry was only to the Jews can be found in his commands to his followers:

Mat 10:5 These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into any city of the Samaritans enter ye not:
Mat 10:6 But go rather to the lost sheep of the house of Israel.

Peter also reiterates the “Jews only” position and helpfully sums up Jesus’ ministry:

Act 3:25 Ye are the children of the prophets, and of the covenant which God made with our fathers, saying unto Abraham, And in thy seed shall all the kindreds of the earth be blessed.
Act 3:26 Unto you first God, having raised up his Son Jesus, sent him to bless you, in turning away every one of you from his iniquities.

And again in Acts 10:

Act 10:36 The word which God sent unto the children of Israel, preaching peace by Jesus Christ: (he is Lord of all:)

The Bible, despite inferences in Luke 4, seems to be of an unanimous position that Jesus was sent only to the Jews. Even the one person who has the most stake in the Gospel to the Gentiles, Paul, claims that Jesus was sent to the Jews. Jesus was sent to the Jews alone.

How then should we take Josephus? Ignoring claims of Eusebius adding text, it could be the case that Paul (who died in 64 AD) had a large immediate influence in Christianity. He did the most traveling of all the apostles and the Gospel spread like wildfire among the Gentiles. When Josephus wrote Antiquities of the Jews (93AD, almost 30 years after Paul’s death), there was probably a large Gentile following of Christ, especially in Rome (to whom the book of Romans was written). Josephus could be referring to this group of people or could have using his current prejudices to project who the followers of Christ would have been.