The ruling dynasty that the Herodians supported was begun by Julius Caesar in 47 B.C. when he appointed Antipater I the Idumaen to be procurator of Judea. His son Herod (the Great), although appointed King of Judea (King of the Jews) in 40 B.C., did not begin to rule Judea until 37 B.C. Herod Antipas, son of Herod the Great, became tetrarch of Galilee and Perea in 4 B.C. after the death of his father. It was this Herod who jailed and beheaded John the Baptist and who sent Jesus to Pilate after his arrest.
Jesus, early in his ministry, attended a synagogue on the Sabbath where he healed a man's withered hand. The Pharisees who saw the miracle believed Jesus broke the Sabbath because they considered the healing "work." Jesus' trespass of their man-made rules (not God's law) motivated their hard hearts to seek the help of the Herodians to murder him (Mark 3:1-6). This is the first plot against Jesus mentioned in the gospels and the first time the followers of Herod are mentioned in the New Testament.
On another occasion the Pharisees wanted to try and trap Jesus into stating something which could be construed as being against the Roman government. Their plan was to send some of their disciples and some Herodians to Jesus and have them ask him a certain "honest" question (Matthew 22:15-16, Mark 12:13-14). The question was: "'Teacher, we know that You are true, and care about no one; for You do not regard the person of men, but teach the way of God in truth. Is it lawful to pay taxes to Caesar, or not? Shall we pay, or shall we not pay?'" (Mark 12:14-15, NKJV). Jesus' response not only did not entrap him but had those who asked the question marveling at his answer!
"All the friends of the family of Herod were opposed to Christ, and ever ready to join any plot against his life. They remembered, doubtless, the attempts of Herod the Great against him when he was the babe of Bethlehem, and they were stung with the memory of the escape of Jesus from his bloody hands. " (comments on Matthew 12:14)
Jesus warned his disciples about the Herodians (Mark 8:15).
The Pharisees wanted Jesus to prove he was the Messiah by giving them a sign or performing a great miracle (Matthew 12:38-40, 16:1-4). Herod, who saw Jesus after his arrest, also desperately wanted to see Jesus perform a miracle "on command" as it were.
8 Herod was very pleased when he saw Jesus, because he had heard about him and had been wanting to see him for a long time. He was hoping to see Jesus perform some miracle. (Luke 23:8, TEV)
The leaven Jesus warned of, according to Matthew Henry's Commentary, was that the Pharisees wanted a heavenly sign; and that Herod had long desired to see Jesus perform a miracle on command (Luke 23:8). The leaven was also symbolic of the Pharisees' and Herodians' teachings (Matthew 16:12) and their opposition to the gospel.