Mark 14:1-2 (ESV)
It was now two days before the Passover and the Feast of Unleavened Bread. And the chief priests and the scribes were seeking how to arrest him by stealth and kill him,  for they said, "Not during the feast, lest there be an uproar from the people."
Mark is very specific about when the chief priests and scribes met. There were only two days left before the Passover. They had to act quick. If they did it during the feast, when it might have been easiest to find him, the people would be in an uproar. The people honored the feast. It wasn’t a time to be going about official business, or trying criminals. The people seemed to like Jesus even if the officials didn’t. However it is fairly safe to say that many aligned themselves with the scribes and priests. Some may have been on the fence. Timing is everything. If they do it during the Passover even those who don’t like Jesus will be upset. It’s like canning a conservative Lutheran Talk show in the midst of Holy Week, its bound to get even those who don’t listen to the show just a bit upset. Probably gained a few listeners.