Why is Cassius nervous about his conversation with Popilius in Act 3, Scene 1 in Julius Caesar? What excuse do the conspirators use to approach...

Cassius is nervous that Popilius might tip someone off about their impending assassination. The assassins surround Caesar with a plea for Cimber, and Caesar blows them off.

The conspiracy to assassinate Caesar is a secret, and the men have been planning for over a month. With that many people involved and that amount of time, there is always a risk that something could go wrong. Someone could find out and tell Caesar, and the game would be up. In fact, Artemidorus does try to warn Caesar, but he is too late and Caesar ignores him.

When the conspirators are approaching the senate’s meeting at the capitol, Popilius Lena tells Cassius that he wishes him luck with his “enterprise.” This spooks Cassius and Brutus both, who worry that Popilius is going to tell on them.

BRUTUS

What said Popilius Lena?

CASSIUS

He wish'd to-day our enterprise might thrive.
I fear our purpose is discovered. (Act 3, Scene 1) 

He doesn’t. Apparently Popilius really does just hope that the assassins succeed. He is on their side, but Brutus and Cassius are even more on edge after this incident. There are a lot of parts of their plan that can go wrong. What if Antony is not waylaid, or Decius Brutus can’t talk Caesar into coming to the capitol? Cassius is so nervous that he says he will kill himself if anything goes wrong.

The plan proceeds, however, without a hitch. The senators who are involved in the conspiracy all have their hidden daggers, and they surround Caesar under the guise of needing to talk to him about a suit. Metellus Cimber has asked Caesar to pardon his brother, who has been banished. Not suspecting anything, Caesar just tells him he will not change his mind.

These couchings and these lowly courtesies
Might fire the blood of ordinary men,
And turn pre-ordinance and first decree
Into the law of children. Be not fond,
To think that Caesar bears such rebel blood
That will be thaw'd from the true quality
With that which melteth fools … (Act 3, Scene 1) 

As far as Caesar is concerned, only weak men change their minds. Flattery will get Publius Cimber nowhere. Banished he is, and banished he will remain. As the senators get down on one knee and beg, Caesar is confused and angry. He is particularly baffled that Brutus would beg and kiss his hand.

Once they have surrounded him, Casca stabs Caesar and then all of the other senators involved in the conspiracy follow suit. Brutus is the last one to stab. All in all, Caesar is stabbed thirty-three times (at least according to Octavius). He is dead in minutes. Brutus and the others celebrate their act as tyrant-killers.