There are a lot of problems with the way you're thinking about the Republican world, and consequently with the way you've framed this question. For one thing, no scholar would describe the Gracchi and Sulla as "liberal" and "conservative"--those words don't even mean the same thing on either side of the Atlantic! Descriptions like this are so often used of people who are or are not seen by modern interpreters as supporting or opposing some concept of "the people," which often differs quite drastically from what the Romans themselves thought about the populus or the plebs. People who establish agrarian laws, to use one example of "liberal" legislation, are considered "liberal" or "progressive." But at best agrarian laws benefited only a particular portion of the population--the urban plebs preferred colonies, in which they could resettle, rather than agrarian distributions, which routinely parceled out land to rural dwellers. At worst agrarian bills where unambiguously anti-populist--Caesar's decemvirate bill in 59 established distributions and colonies pretty much solely for Pompey's soldiers, and Caesar was famously despised by the urban plebs (and likely the rural, who were the ones giving up their property) during his consulship. The Gracchi were staunch aristocrats, from one of the most distinguished plebeian senatorial lines and with a direct line of descent from Scipio. This alone doesn't disqualify them from anything, but it's worth noting that Sallust separates them and their legislation from later individuals who are often compared to them. Ti. Gracchus failed to win over the urban plebs with his agrarian bill which had nothing to do with them, and when his supporters were occupied at election time with the harvest he was forced to resort to violence to disperse the elections. While he himself used tribunician power with great effect he also established that tribunician power could be superseded and stripped. Whatever he causes for Octavius' opposition (one suspects that a significant portion of the urban plebs was against the bill, though our literary sources rarely make a distinction between the groups of the faceless mass of the plebs), Ti.'s actions against him acted wholly against the principles of plebeian political activity. C. Gracchus fared somewhat better than his brother, establishing a modest grain law, a handful of colonies, and laws de provocatio alongside his own agrarian bill in a much more carefully considered and comprehensive package. But he also limited the power of the tribunes, by removing their power of veto over the distribution of consular provinces. And while it's again hard to say how popular he was among the urban plebs it's worth noting that few of them came to his aid when he was killed and Livius Drusus' much more spectacular colonial bill was thought to have drawn a lot of crucial support away from C. Sulla's removal of tribunician power is talked of as being "conservative," but in what way? The tribunate was an ancient office, predating the praetorship and quaestorship--it was the fundamental representation of the conclusion of the Conflict of the Orders some centuries earlier. And Sulla doubled the size of the senate, introducing hundreds of equites into the curia--a typically popularis move, given the status of equites as wealthy non-senatorial plebeians, and one for which previous politicians had gotten in great trouble for. Livius Drusus' (the younger) legislative package had proposed the exact same provision, the introduction of several hundred equites into the senate, and was one of the things that got him murdered. Moreover, Sulla doubled the number of lower magistracies, increasing competition for the highest offices but also decreasing the power of all magistracies before the consulship. What can be said to be "conservative" about any of this? Indeed, many of these provisions were agitated for by violent populares during the decades before.

Apart from the difficulty of arguing for an understanding of "conservative" and "leftist" politics in the Republican world, and of assigning individuals (who, in typically Roman fashion, neither had to be nor really ever were consistent or required to have stated ideologies) to either camp, we're also faced with the issue of the "eventual collapse" of the Republic. Syme considered the "Roman revolution" as more or less of an inevitability, and Meier agreed that if Caesar had not come along someone else would've. But there's not really much reason to think so teleologically, and there's a lot of resistance these days. The Republic had weathered the storm of factional strife before (I highly recommend, if you can read German, an article by Ungern-Sternberg called Die legitimitätskrise der römischen republik, which among other things lists something like eleven similar crises before the Gracchi) and had emerged stronger than ever. The Republic, with its use of popular legislative assemblies and annual magistracies, was capable of very rapid change in order to keep itself alive. Syme pointed to the lack of concern among the senatorial class for the workings and security of the state. But this had always been the case, and it's worth pointing out that Sallust's oft-quoted concept of the metus hostilis doesn't really work. Carthage in 146 hadn't been a cause for fear in more than a generation, and in the fragments of the Histories Sallust actually seems to back off from this idea, portraying the Hannibalic War as a brief interlude between periods of factional strife stretching back to the beginning of the Republic. The supposed loss of concordia lamented by many commentators ancient and modern that occurred with the Gracchi can neither be reliably dated to them nor can it so straightforwardly be described as having existed in the first place. The Gracchi were not the first to emphasize a gap between the senate and populus in the political sphere. In fact, during the Punic Wars, this supposed time of concordia, some of the most important factional fights of this kind were going on. C. Flaminius, cos. 223 and 217, a novus homo, passed as tribune in 232 a bill distributing the ager Gallicus. He was voted a triumph by the people, not the senate, and notably supported the lex Claudia of 218, a tribunician bill that imposed stricter limits on the ability of senators to own ships (and thus engage in commerce directly). It's notable that Polybius describes Flaminius in many of the same ways that later writers describe the Gracchi, as the cause of a destruction of concordia and a moral decline. This right in the middle of the supposedly unified period of the Punic Wars! This perception is echoed by the fragments of, say, Cato the Elder and other early Latin authors. The perception of a declining Republic was not one unique to late Republican authors, which should influence our understanding of their statements of doom and destruction.

So, you're asking for consensus? There isn't even consensus that the Republic was collapsing in the first century, much less that it was an inevitability. Well into 49, several months after Caesar had effected his lightning march through Italy in January, Cicero expressed the opinion in his letters that he believed Caesar and Pompey could come to an agreement. That they didn't had little to do with the institutions of the Republican state.