There are several indications in Julius Caesar that the murder of Caesar is a bad idea.
To begin with, in Act I, Scene 1, the behavior of the commoners indicates that they idolize Caesar. Even though they are fickle, at the present time they are basically on Caesar's side, and unlikely to desert him unless they can be won over by a more popular leader.
A second reason the plot is a bad idea is that the plotters' motives are different. Brutus is motivated purely by his perception of the public interest -- he will not even bind the conspirators by an oath (Act II, Scene 1) -- while Cassius, as Caesar correctly notes, is driven by envy of Caesar and a desire to pull down a man who has risen far above him. When Cassius first hints at the plot, Brutus realizes this divergence of motive between them:
Into what dangers would you lead me, Cassius,
That you would have me seek into myself
For that which is not in me? (Act I, Scene 2)
However, he later succeeds in talking himself into the idea that the plot is a good thing by his own standards (Act II, Scene 1), and puts aside these qualms.
A third reason, which grows out of the second, is that the plotters cannot agree on an approach that will neutralize opposition and win over the Roman masses. In particular, Brutus wants to keep everything noble and thus opposes the elimination of Mark Antony. This, as Cassius correctly anticipates, is a gross error (Act II, Scene 1; Act III, Scene 1). Antony's speech at Caesar's funeral elevates him to the position of Caesar's heir with the crowd (Act III, Scene 2), and eliminates the possibility of the conspiracy gaining mass support.
The fourth and perhaps the most important reason is that Caesar is not just an ambitious individual, but the representative of a social trend. As the success of Antony and Octavian indicate, Roman society could no longer be ruled by the same methods it had been before. The mob had become fixated on personalities, not politics in the old sense. It seemed to need a strong man, and if that man were not Caesar, it would be someone else.