I think I'm pinning my ribbon on SM for this one - there was no need for him to beg to Snape for public show - he would have done that via occlumancy etc ..
The beg was genuine - do the job we discussed Snape - please ...
That is the only way and reason Dumbledore would have used his last words to beg in my mind - there was no merit in humiliating himself - Snape will score the biggest respect with Voldemort just by doing the job - the fact he was begging wouldn't matter given the overall result!
Okay, so I spent a very long time rereading this entire thread! Shoo!!!
I blew the dust off this comment as I still feel that something more then Dumbledore's verbal pleading passed between him and Snape just before Snape shot the fatal spell.
HBP - The Lightningstruck Tower pg. 595
"Severus . . . "
The sound frightened Harry beyond anything he had experienced all evening. For the first time, Dumbledore was pleading.
Snape said nothing, but walked forward and pushed Malfoy roughly out of the way. The three Death Eaters fell back without a word. Even the werewolf seemed cowed.
Snape gazed for a moment at Dumbledore, and there was revulsion and hatred etched in the harsh lines of his face.
"Severus . . . please . . ."
Again, we see things through Harry's eyes. He took Dumbledore's verbal words as pleading, but there was a pause there when the two of them only looked at each other. We see that Harry perceived Snape's look as one of revulsion and hatred, but has JKR once said throughout the entire series that Snape ever smiled? I don't think so! He sneared quite often, but I don't think he ever once smiled!
If during that moment of silence, Dumbledore was communicating with Snape the fact that he had to do the deed, thus the look on Snape's face. We see it through Harry's eyes, but we know how Harry has always felt about Snape.
It was all a set up! I believe the set up went on all year, thus Dumbledore's words to Harry that he was to always have his invisibility cloak on him wherever he went all year. It was quite fortunate that he had it on at the time that Draco came to the tower.
Also, remember how Snape went up on the tower. Hermione and Luna were watching Snape's office, but we never actually found out that he harmed anyone in order to get on the tower, other then Stupefying Flitwick. He didn't even seem know the Death Eaters were in the castle until McGonagall sent Flitwick down to get him.
When it was over, Snape went down from the tower after the other Death Eaters and ran out of the castle. Of course, the other teachers would not shoot at Snape unless he did something before them like shoot a spell at someone. They thought Snape was chasing the Death Eaters. Hagrid even commented on that. But to our knowledge, until Snape faced Harry on the grounds, he did nothing like that. He simply ran down from the tower and out of the castle behind Draco and the Death Eaters.
I think that moment of silence as Snape stared at Dumbledore was a time for Dumbledore to give Snape his final instructions and possibly a bit of encouragement to do what he needed to do!