"When they had assembled with the elders and consulted together, they gave a large sum of money to the soldiers" (Matt. 28:12). What a sad cover-up! Rather than being honest and desiring to know the truth, they would rather lie and deny everything. The Jewish authorities evidently believed the guards or else they would have denounced them before Pilate. Thus, they knew that Jesus was raised from the dead. This partly explains why later "a great many of the priests were obedient to the faith" (Acts 6:7).
"Tell them, 'His disciples came at night and stole Him away while we slept'" (Matt. 28:13). There is a logical fallacy in their cover-up story: How would they know what actually happened to the body if they were sleeping? But that is the best story they can fabricate so they run with it.
"And if this comes to the governor's ears, we will appease him and make you secure" (Matt. 28:14). The Jewish leaders couldn't risk telling Pilate the truth because he might believe it and spoil their cover-up. If they told Pilate and he didn't believe them, then he would have had the soldiers slain for their failure to guard the tomb. If that happened then the Jewish authorities wouldn't have any "witnesses" to circulate this cover-up story. Therefore, they felt like the best thing was to try to cover-up the truth and pay these soldiers some bribe money. Surely, this truth in and of itself is a testimony to the fact that Jesus was resurrected. How else could soldiers get paid extra for failing to do their job? What a scandal! If Pilate did hear about the matter, the Jewish authorities would appease him, perhaps with a bribe.
"So they took the money and did as they were instructed; and this saying is commonly reported among the Jews until this day" (Matt. 28:15). The wording seems to indicate that this story was widely circulated (i.e., beyond the borders of Jerusalem).