In Julius Caesar, what is Brutus deliberating in Act 2, Scene 1?

"Whet" means to "sharpen by rubbing against as if a knife or to stimulate" according to Webster's Dictionary.  By this definition, Brutus has been "sharpened or stimulated" against Caesar by Cassius.  Cassius has been in Brutus' ear about all the bad things Caesar has done and what it might mean for the future of Rome if something is not done about it.

Since Cassius has begun all this talking, planting the seed of conspiracy and rebellion, Brutus can think of nothing else.  The entire quote is:

Since Cassius first did whet me against Caesar, I have not slept.  Between the acting of a dreadful thing and the first motion, all the interim is like a phantasma, or a hideous dream.

They have been in his ear, they have left letters for him to find, they have been after him to act on behalf of Rome against the tyrant who would enslave them all with his notions of government.  This quote opens at the Ides of March dawns...little time is left for Brutus to make up his mind if he will act with or against the conspirators.  He is under pressure, can not sleep, and is plagued with horrible visions of what will happen--either way he is tortured.  The visions are not good no matter whose side he is on.  Hallucinations and hideous dreams are no one's friend. 

In Julius Caesar, what is Brutus deliberating in Act 2, Scene 1?

To understand the quote, it would probably be best to read it in its entirety:

"Since Cassius first did whet me against Caesar,
I have not slept.
Between the acting of a dreadful thing
And the first motion, all the interim is
Like a phantasma or a hideous dream.
The genius and the mortal instruments
Are then in council, and the state of man,
Like to a little kingdom, suffers then
The nature of an insurrection."

Brutus is considering the fact that ever since Cassius included him in the conspiracy to kill Caesar, he has not slept.  He says that the waiting for something awful - "the interim" - is like an awful dream, and it is keeping him from sleeping at night.

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What is Brutus pondering at the start of Act 2, Scene 1 in Julius Caesar?

He is contemplating the murder of Julius Caesar. He says:

It must be by his death: and, for my part,
I know no personal cause to spurn at him,
But for the general. He would be crown'd:
How that might change his nature, there's the > question:/

What question is Brutus pondering at the start of Act 2, Scene 1 in Julius Caesar?

In act 2, scene 1, Brutus is pondering whether or not to join the conspirators to assassinate Julius Caesar. Brutus contemplates the difficult question and begins by mentioning that he has no personal grievance against Caesar. However, Brutus also acknowledges that crowning Caesar king could be a mistake. Brutus also contemplates Caesar's ambition and realizes that Caesar may feign humility until he reaches the highest office, where he can change into a ruthless tyrant. Brutus goes on to frame the argument that his quarrel with Caesar is with his potential behavior and likens Caesar to a "serpent’s egg," which is extremely dangerous when hatched. In the end, Brutus concludes that assassinating Caesar will prevent him from turning into a tyrant, disbanding the Senate, and oppressing the Roman populace. Therefore, Brutus decides to join the conspirators and is willing to murder Caesar before he has the opportunity to act as a ruthless tyrant. Unlike the conspirators, Brutus's intentions are pure and he genuinely believes assassinating Caesar will preserve the Roman Republic.

What question is Brutus pondering at the start of Act 2, Scene 1 in Julius Caesar?

The beginning of Act Two takes us to the eve of the Ides of March.  Brutus is awake through the night, periodically asking Lucius, his servant, for either items or information.

The major question that Brutus is pondering at this point is whether or not to join the other senators in the assassination of Julius Caesar.  In the scene, Brutus weighs the issue.  On the one hand, Caesar is a good friend, and he does not want to betray the trust that Caesar has placed in him.  On the other, Brutus trusts the other senators, and Cassius in particular.  Their assertions that the people want Caesar removed from office weigh heavy on Brutus' mind as the night wears on.  Eventually, Brutus will choose to join the others in their assassination plot, setting the stage for later actions to come.