Several Jewish leaders question Jesus. By asking whose authority Jesus is acting under they are simultaneously questioning any authority of Jesus and placing their authority over his. Jesus, knowing that the time of his crucifixion is not quite yet, turns the question back onto them: What about John the Baptist?
This puts a problem upon them for the two reasons stated in the text, but it warrants further explanation. John’s baptism signaled a rejection of Judaism as it existed. Baptism, for the Jewish mindset, was a reserved for converts to Judaism. It was a washing away of the past in order to pursue a new future once they had found God. While circumcision was for men only, baptism was for everyone. By being baptized, Jewish people were rejecting the Judaism currently being practiced and in so doing were acknowledging God was doing something new. This is why baptism was a sign of repentance.
By putting the question to the Jewish leaders, Jesus questions their authority to even question him. If they accept the baptism was from heaven, they lose all authority because they are part of the system John’s baptism was meant to reject. Yet they fear they will lose power due to a rebellion if they reject John’s baptism. This is why they issue the ambiguous “we don’t know.” It would cost them too much to respond one way or the other.
So it is with us. Too often we seek a political answer when there should be one. We know the right thing to do, and when we know that thing and don’t do it, it is somehow worse than outright rejecting it.