Jesus and the Gentiles

I often wonder about the meaning of the passages in the Gospels where Jesus states that he only came to the lost sheep of the house of Israel.

Is it possible that St. Paul invented the notion that Jesus's message was universal and ought to be spread to the Gentiles as well? Especially given the pervasive theory that Paul's visions were the result of epileptic fits, is it possible that Jesus never actually saw himself as the proclaimer of a universal message, but rather simply as a Jewish sage? My main question is what evidence do we have that the notion that the Gentiles ought to be evangelized was not simply invented by Paul, and that passages such as John 3:16 and Matthew 28:19 were not simply written as a reflection of a Pauline view of Christ, rather than as an accurate description of how Jesus himself viewed his mission.

Response:  There are so many instances in the Gospels of Jesus reaching out beyond the Jews that it is impossible to (sensibly) believe that they are all fabricated. Consider the Woman of Samaria for example.