I can see this happening in a couple of ways, or a mixture.
First possibility I believe is feasible is Spartacus, akin to Eunus in the first servile war, proclaims himself a prophet and appeals to both slaves and impoverished plebeians (off the back of the Populares). He either dies a martyr or has substantially more success. His 'religious' teachings serve the basis for emancipation sooner or later.
Second, the more radical side of the Populares have far more success - the contradiction between slave land armies working the latifundia and the masses of unemployed plebeians is resolved in another manner than Augustus' large public works and the Marian reforms to the army.
Third, some combination of the two - I think Spartacus going full warrior Jesus and addressing and appealing to the plebs in the manner of Tiberius Gracchus is both fascinating nor implausible. I find Tiberius' speech fragments incredibly insightful to radical political thought at the time:
"The savage beasts," said he, "in Italy, have their particular dens, they have their places of repose and refuge; but the men who bear arms, and expose their lives for the safety of their country, enjoy in the meantime nothing more in it but the air and light and, having no houses or settlements of their own, are constrained to wander from place to place with their wives and children." He told them that the commanders were guilty of a ridiculous error, when, at the head of their armies, they exhorted the common soldiers to fight for their sepulchres and altars; when not any amongst so many Romans is possessed of either altar or monument, neither have they any houses of their own, or hearths of their ancestors to defend. They fought indeed and were slain, but it was to maintain the luxury and the wealth of other men. They were styled the masters of the world, but in the meantime had not one foot of ground which they could call their own" - from Plutarch's Parallel Lives
Regarding how this pans out with class relations I can see as has already been stated either colonii happening sooner, indentured labour and extended patronage and clientele systems.