These are great citations from RW to give you a direct answer to your question. The political mood is as varied as the Roman citizens who occupy it.
The question that might be interesting for you to explore so you can do some deeper, critical, and independent thinking, is why the entire play begins with Flavius and Murellus trying to silence the raucous Roman plebeians. As RW notes, these two tribunes are eventually silenced. The plebeians also joke and challenge the authority of the tribunes, somewhat subtly, but they are rude enough, oblivious enough to the fact they once cheered Pompey, now dead, enough that Murellus unleashes on them with "you blocks, you stones."
So chew on this: the poorer citizens are partying, and then they are chastised by their superiors and chased away, who are later also punished.
What might Shakespeare be showing us about the average citizens and the nature of their behavior when it comes to honoring leaders and understanding who's truly leading them?
What might Shakespeare be showing us about the nature of political power and how it changes hands?
And what might he be showing us about how those who speak out in ancient Rome are treated? (Keep in mind that there wasn't a lot of free speech in Elizabethan England, either, so it's not a guarantee that Shakespeare is recommending that Flavius and Murellus be allowed greater freedom. Or is he? You have to weigh evidence from the whole play to determine what stance he might be taking.)
Last thought: compare the first scene of the play to the last scene. What has happened? How does the mood of this scene compare to the opening mood?
Well, the mood on the streets is riotous. Caesar has returned from a triumph against Pompey. The commoners are out on the streets celebrating his triumph. Yet he is so popular with the people that Cassius and Brutus are worried that Caesar might be chosen as a king - giving him a tyrannous power over Rome.
Even in the first scene, the mood of the commoners is split up by two malcontents, Flavius and Marullus:
Go you down that way towards the Capitol;
This way will I. Disrobe the images,
If you do find them deck'd with ceremonies.
Some people celebrate Caesar. Some are trying to limit his power. And that's true too of Brutus and Cassius. Antony is absolutely for Caesar:
When Caesar says 'do this' - it is performed.
Cassius, on the other hand, subtly goads Brutus into questioning Caesar's dominance over Rome, agreeing with him that they don't want Caesar to take the crown - but also asking why Caesar is so dominant:
'Brutus' and 'Caesar'. What should be in that 'Caesar'?
Why should that name be sounded more than yours?
Write them together: yours is as fair a name...
The political mood is clear: Caesar is becoming ever more powerful. And as he does so, more and more people are starting to wonder whether his power should not be limited. Flavius and Marullus, for pulling scarves off Caesar's images, are "put to silence". The conspiracy springs up secretly because any open opposition to Caesar will meet with their own solution to his power: death.