Frankly, you can forget a lot of the big names: one of the things killing the Republic was entirely economic, and how it lead to an economic state of affairs that negated the assumptions of the Roman constitution.
The wars in Spain, simply put, unglue the Republic. Men are serving abroad for years. There farms go under. They go under at the same time men are coming back from Spain with a lot of cash and slaves. Their farm is bought, and amalgamated with their neighbors, and staffed by slaves. If your farm survives, well, tough - the new magnate wants it, can send men to take it, and can make damn sure your suit in the law courts in room doesn't work. And if you do win, he'll repeat the process.
This economic dynamic dooms many of the reformers, because they're one reform idea is to break up the public lands, distribute them to farmers... and then draft them all for another multi-year campaign in Greece or Anatolia, while the same cycle repeats in Italy, as of course the imperator is coming back with even more loot and slaves.
The Roman constitution assumes a large mass of freeborn citizen farmers, some considerably wealthier than the others, many owning some number of slaves, but ultimately, a number of farmers numbering in the tens of thousands able to purchase their weapons and support their drilling. This farm had to be solid enough finance the metal in the arms, and on good enough footing to allow some of its men to loose a growing season to the legions. Rome's conquests outside of Italy make this small farmer about as likely to survive as steak at a bear convention.
These farmers than move to Rome. Where they become clients of the men who took their farm, and reliant on the grain dole... or selling their vote to the rising magnates. Or join the legions.
When the choice is poverty or the legions, the legions will win. When the only way up for the legionary is the spoils of war, the imperator will find them. When the imperator has a loyal army at his back, he will use it. And the people the Republic required to be loyal to it, to prevent a rex? Their now soldiers in that imperator's army.
To be blunt, what Grachus wanted or what Cicero wanted in this context does not matter. Their political system was set up for an economic and social dynamic that was completely lost by 130. The rest is history.