But I am constant as the northern star

Friends, Romans, countrymen, lend me your pants!

An owl hoots in the public square at noon. A lioness gives birth in the streets. A man's hand burns with flame without being scorched. The dead leave their graves. No wonder Calpurnia had a nightmare the evening before the ides of March. I'd freak too if I dreamt that people were bathing in my husband's fountain of blood.

Caesar, however, is so high from the public's very public adoration of him that he spurns the soothsayer's warnings and his wife's pleas (along with speaking in the first person) and goes to the capitol with Brutus and all his senate buddies anyway.

Earlier in the play, while listening to Casca roundly freaking out over the strange portents floating around the city, Cicero says,

Indeed, it is a strange-disposed time; 

But men may construe things after their fashion, 

Clean from the purpose of the things themselves.

And Cassius says to Brutus:

The fault, dear Brutus, is not in our stars, 

But in ourselves, that we are underlings.

In one way, Caesar is taking it upon himself to ignore the "stars" that are telling him to phone in sick on the ides. Unfortunately, he is also feeding into his own tragic fault: he believes himself to be a thing of the heavens, so powerful and untouchable that he fails to recognize his own human frailty. Moments before he is stabbed on the marble floor of the Capitol, Metellus Cimber, Marcus Brutus, Cassius, and Cinna beg Caesar to repeal Publius Cimber's banishment. Caesar, surrounded by these politely dissenting voices, refuses, citing himself as something as unmovable as Olympus.

Again, with the astronomical references. I love 'em.

Julius Caesar, Act III, Sc. I

Caesar: I could be well mov'd if I were as you.
If I could pray to move, prayers would move me.
But I am constant as the northern star,
Of whose true-fix'd and resting quality
There is no fellow in the firmament.
The skies are painted with unnumb'red sparks.
They are all fire and every one doth shine,
But there’s but one in all doth hold his place.
So in the world. 'Tis furnished well with men,
And men are flesh and blood, and apprehensive,
Yet in the number I do know but one
That unassailable holds on his rank,
Unshak'd of motion. And that I am he
Let me a little show it even in this:
That I was constant Cimber should be banished,
And constant do remain to keep him so.