How did Dimmesdale respond to Pearl's question in The Scarlet Letter?

In The Scarlet Letter, the most important exchange of information that occurs between Pearl and her (unbeknownst to her) father, Reverend Dimmesdale, takes place in chapter 12, "The Minister's Vigil".

During this chapter, Dimmesdale walks toward the scaffold where Hester stood the first time around, seven years earlier. He realizes that he should have been there standing with her back then. He is filled with guilt and anger, and he cries really loud in a sign of desperation. His cries are seldom heard, and the night goes on, as usual.  

Hester and Pearl are nearby. Hester was tending the deathbed of Governor Winthrop and, upon leaving, crosses the scaffold and finds Dimmesdale there. This is one of the rare occasions where the triad of Dimmesdale-Hester-Pearl are alone, together. It is also an even rarer occasion, because, they embrace in a way that the author describes as "electric". This is an allusion to the fact that maybe for once, the three have finally connected at a higher level. 

In a somewhat anticlimactic moment, Pearl asks whether Dimmesdale will also stand with them on the scaffold the next day at noontide, and will he also hold their hand the way that he is doing now. 

Wilt thou stand here with mother and me, to-morrow noontide?” inquired Pearl.

To which Dimmesdale responds,

“Nay; not so, my little Pearl!”  “Not so, my child. I shall, indeed, stand with thy mother and thee one other day, but not to-morrow!”

The reason why this is an anticlimactic response is because the reader would have expected Dimmesdale to have arisen to some degree of dignity, accepting, for once and for all, what he did by admitting to the villagers that he had been living a lie. 

However, Hawthorne is consistent in his characterization of Dimmesdale as a coward, and this is evident when he describes the reason why Dimmesdale responds like that to Pearl:

...the new energy of the moment, all the dread of public exposure, that had so long been the anguish of his life, had returned upon him; and he was already trembling at the conjunction in which—with a strange joy, nevertheless—he now found himself.

Hence, here we find Dimmesdale, yet again, in his response to Pearl, denying his sin and going back to a life of hypocrisy and lying. His public persona continues to matter to him more than anything else.