On a practical (halachic) level, there was the consideration that amei haaretz (or at least a significant minority of them) were known to be careless about separating maaser from their produce (most of Maseches Demai deals with the ramifications of this), and about the laws of tum'ah and taharah (which, in fairness to them, can be pretty complex).
So just to be a ne'eman (someone who can be trusted about maaser) already meant a degree of social separation from the amei haaretz - specifically, not being a guest in his house. To be a chaver (someone who can be trusted about tum'ah and taharah as well; this term is also often used for Torah scholars) required still more: restrictions on what kind of produce he could buy from an am haaretz or sell to him, and not having an am haaretz as a guest in his house unless he'd change his clothing first (Demai 2:2-3) - the clothing of an am haaretz is a source of tum'ah (Chagigah 2:7); the wife of a chaver would have to keep away from her am haaretz friend when it came to kneading dough (Sheviis 5:9/Gittin 5:9); and there were other complex rules when it came to having an am haaretz in your house, about what might or might not have become tamei (Taharos chs. 7-8).
So that alone must have fueled some of the resentment of the amei haaretz towards the Torah scholars - but these halachos could not be compromised if the talmidei chachamim were to preserve their tahor status. (Which is why this isn't an issue today, when we are all tamei anyway.)
We do find some cases where they worked with individual amei haaretz or small groups of them. One example is R. Zeira in Sanhedrin 37a doing "kiruv" with his local gang of toughs, where the upshot was that after his death they finally did teshuvah. But after all, that could be taken either way! You could argue that his work with them planted seeds that finally bore fruit, but you could equally well argue that it was their fear of complete ostracism by the rabbis that induced them to do teshuvah ("until now we had [R. Zeira] to pray for us, but now, who will do so?"), and thus that his attempts were counterproductive and delayed their teshuvah. (I heard this explanation in a shiur; I don't know the source.)
So it may be that the difference has something to do with the relative positions of the Torah scholars and the amei haaretz in society. As long as the former were generally accepted as the elite and the establishment, then it may indeed have been more likely that the amei haaretz would seek them out and try to improve themselves for this purpose; nowadays, when this situation no longer obtains, there is really no choice but to get ourselves involved and try in whatever ways we can to upgrade their knowledge and observance of Judaism.