Jesus did not spend the night in Jerusalem because it would have been too dangerous to do so. Jesus did stay in Bethany (cf. Matt. 21:17), perhaps several nights. However, if He did such it is likely that He didn't always stay in the same house. Otherwise it would have been easy for the religious leaders to learn of His whereabouts and have Him arrested at night when the multitude wasn't around to "protect" Him.
It is also possible that Jesus and His apostles spent some of these nights outdoors on the Mount of Olives. The climate at that time of year would have been conducive to such and Jerusalem would have been exceedingly crowded because of the approaching Passover feast. Certainly many Jews slept outside in tents or wrapped up in their outer garments.
The people came to hear Jesus speak in the temple "early in the morning" (Luke 21:38). The excitement of the triumphant entry had not died down after two days; Jesus was still the center of attention.
"Now in the morning, as they passed by, they saw the fig tree dried up from the roots. And Peter, remembering, said to Him, 'Rabbi, look! The fig tree which You cursed has withered away.' So Jesus answered and said to them, 'Have faith in God'" (Mark 11:20-22).
On Tuesday morning, as Jesus and His disciples headed back toward Jerusalem, they passed by and "saw the fig tree dried up from the roots." The disciples were amazed at this sight and asked - "How did the fig tree wither away so soon?" (Matt. 21:20). It had only been one day, and this rate of decay was not natural (rather, it was supernatural).
Peter mentions that this was the tree Jesus had cursed. Certainly they all were aware of this, yet they were still puzzled about the miracle. Thus far they had not witnessed any miracles other than ones of mercy. This miraculous act was one of judgment and the disciples desire that Jesus speak more about it.
Jesus begins to explain the miracle He performed against the fig tree with this statement - "Have faith in God." The implication is that the fig tree would not have withered so soon had it not been for His faith in God. He then goes on to teach some general principles about faith, prayer, and miraculous power, which we will consider in our next lesson.