In Julius Caesar, does Caesar seem to be aware that something is not right at the senate?

Caesar is clearly uneasy at the beginning of the play, as illustrated by his remarks to Antony when he calls to him:

Let me have men about me that are fat;
Sleek-headed men and such as sleep o' nights:
Yond Cassius has a lean and hungry look;
He thinks too much: such men are dangerous.

Antony assures him that Cassius is a good Roman and that he has good intentions. Caesar, is, however, cynical, and replies:

Would he were fatter! But I fear him not:
Yet if my name were liable to fear,
I do not know the man I should avoid
So soon as that spare Cassius.

Caesar justifies his suspicion of Cassius, stating that he is much unlike Antony. He mentions that if he should be fearful, that Cassius would be one of those whom he would avoid. He sees a danger in Cassius, for he is the type of man to resent those who have greater power than he. He wishes to ask Antony more about Cassius since is not fearful of fear itself, but needs to know what there is to be fearful about.

Although he dismisses as a dreamer the soothsayer who warns him of the Ides of March, there are signs that Caesar is not entirely at ease. The next morning, for example, prior to his leaving for the senate, he instructs a servant:

Go bid the priests do present sacrifice
And bring me their opinions of success.

Caesar wishes the priests to provide him with guidance and, by reading the entrails of a sacrificed animal, inform him what the day will bring. This was common practice if one wished to predict good or bad fortune. Caesar is obviously concerned, especially since Calpurnia had also advised him about a terrible nightmare she had had about nature rebelling against itself and that his statue was flowing blood. 

His overconfidence, however, makes him reject Calpurnia's pleas not to leave. When the servant informs him about the priests' recommendation that he should not go outside since they could not find the heart of the sacrificed animal (an unlucky omen), he ironically prefers to interpret their prediction positively. It is clear that, although he might be ill at ease, his huge ego gets the better of him. He sees himself as one who is above fear and not afraid of death. 

He eventually complies with Calpurnia's request to humor her, but once Decius Brutus interprets her dream and gives it a positive slant, he is flattered and decides to leave for the senate-house. He is met and accompanied by his soon-to-be assassins, who lead him to his doom.