Luke 20:7

‘And they answered, that they knew not whence it was.'

So they replied lamely that they did not know the answer to His question. Lame though their reply was they were really left with no option. But we can imagine their sense of extreme humiliation at having to do it. For by answering like this they would know that they were admitting that they in fact were in no position to decide on genuine bases of authority when it came to someone like John. And if they admitted that they could not judge John's authority, how could they then be credibly seen as being able to judge any prophet's authority?

Furthermore at the same time the crowds, who were not stupid, would know from their reply exactly what the situation was. To the crowds they would simply be revealing themselves as treacherous. So their whole position was being undermined by their inability to answer, and instead of showing up Jesus they had shown themselves up.

And, of course, the consequence of this was that as they could not decide on what John's authority was, it was quite clear that there was no point in Jesus appealing to that authority. His appeal must await their deciding on John's authority. But it had answered the question. For the crowds, who would know of Jesus' connection with John would again draw their own conclusions. They would accept His authority, both because they accepted John's authority, and because of His own works and teaching.