There was no "populares faction." Popularis is a term used by Cicero to describe an individual who relied on the plebs, either urban or rural, for support at the polls rather than on senatorial approval and the senatorial class. This category was vast and ever-changing. It included most tribunes of the plebs who brought legislation, regardless of their usual political leanings, as well as potentially any politician--Cicero himself adopted a popularis stance in 63 to successfully combat the Rullan bill and the Catilinarians, both of which theoretically should have been in the interest of the plebs. Cicero's example shows quite well that vir popularis was just one of many hats that politicians could put on at different points--nobody expected any popularis to continue to rely wholly on popular votes throughout his career, and with only one or two exceptions no popularis politician remained such for the duration of his career. Tribunes were particularly well known for adopting popularis tactics during their tribunates and then settling into more aristocratic lines of support as they canvassed for higher magistracies like the praetorship--Publius Clodius was met with some surprise when he continued his mob violence past his tribunate. Likewise Cicero's example shows well that there was no particular legislative ideology associated with populares. The Roman world knew no such thing as a political platform--indeed, cases like Publius Clodius' canvass for the praetorship, in which he declared his intention to submit certain bills if he were elected, were decidedly unusual--and rarely do we see the Roman senatorial class unable or unwilling to constantly shift their alignment as the situation required--Cato, as tribune of the plebs, successfully passed a bill for grain distribution that expanded the number of citizens eligible to receive state grain. The label of popularis was one of political tactic, not of political alignment or ideology, and it was a label applied to the individual--the idea of a party or political faction composed of populares is fantasy

Sulla failed to kill Caesar, but not for want of trying. Caesar was connected by marriage to the Marians, and if he did not hold Marian sympathies to begin with he certainly got them during his persecution by Sulla. Sulla could not execute Caesar because of his position as Flamen Dialis, and initially it seems that he would have been satisfied had Caesar simply divorced Cinna's daughter and more or less retired into the position of Flamen Dialis, who was largely outside the circle of political importance due to the strict prohibitions and rules that he had to follow. Plutarch thinks that Sulla allowed Caesar to become Flamen Dialis because he was too busy with the proscriptions to worry about a boy, but Plutarch is wrong--we know from Velleius Paterculus that Caesar had been nominated to the position by Marius and Cinna. When Caesar proved unwilling to divorce Cinna's daughter Sulla annulled Marius' appointment, deposing him (probably illegally) from his priesthood and confiscating his dowry, and Caesar went into hiding. For some time Sullan partisans hunted Caesar while in hiding, and Suetonius says that he was forced to sleep in a different spot every night--the Sullans certainly gave killing him a go. In the end what saved Caesar's life was his flight to Asia. The precise details of what happened are not totally clear. Plutarch thinks that he was nearly captured in Sabine country, and after bribing his pursuers fled down to the coast and sailed to Thermus' camp in Asia. Suetonius thinks that Caesar was given a pardon before he fled, thanks to the support of the Vestals and of Mamercus Aemilius and Aurelius Cotta. Suetonius' versions seems to me to make a little bit more sense, simply because while both he and Plutarch quote Sulla as saying that he saw many Mariuses in Caesar (Suetonius' phrase is nam Caesari multos Marios inesse. Plutarch puts the phrase in the negative--οὐκ ἔφη νοῦν ἔχειν αὐτούς, εἰ μὴ πολλοὺς ἐν τῷ παιδὶ τούτῳ Μαρίους ἐνορῶσι, "He said they were senseless if they did not perceive in the boy many Mariuses--but it's comparable and clearly from the same source) Suetonius places the quotation as after the pardon, as a warning to those of his circle who demanded that Caesar be spared. Plutarch's chronology of the quotation is impossible, since he places it before Caesar's assumption of the office of Flamen Dialis, which is not possible--it seems to me to make more sense in Suetonius' context, although of course it should be noted that an apocryphal quotation like that is no good basis to make an actual judgment. In any case what's clear is that getting the hell out of Dodge is what saved Caesar, whether or not a pardon was ever actually issued--Suetonius agrees that with his priesthood gone Caesar fled to Asia.