It sounds like quite the parable about populism, which makes it very interesting but also raises my skepticism about simple and pat explanations of history.
I don't think you could say that at all really. The legislative programs of both the Gracchi were predominantly focused on the allies and rural plebs, while the urban plebs were an afterthought at best. It's telling that Appian specifically mentions that Tiberius was forced to rely on the urban plebs in his bid for re-election to the tribunate, since his rural supporters were at the harvest--these urban supporters were fairly small in number and not nearly as devoted to his legislative program as the rural voters. Gaius Gracchus in particular does not seem to have been popular with the urban plebs at all. His repeated championing of the rural voters and allies alienated the urban plebs, who did not significantly benefit from distributions of the ager publicus, his infrastructure projects through Italy, and his motions to extend citizenship to the Latins--this last, in fact, was probably quite hated by the urban plebs, who later fought Sulpicius' Italians over a similar issue, the distribution of the post-Social War citizens into their voting tribes. It's telling both that Gaius' citizenship bill failed when a consular order prevented non-citizens from entering the city, and that of Livius Drusus' motions the most successful was his foundation of twelve colonies (as opposed to Gaius' two)--colonial ventures were much more favorable to the urban plebs than land distributions, which generally favored rural communities, and we can clearly see Gaius' urban support (such as it was to begin with) being effectively drawn off to Drusus' much more appealing legislative program. That the urban plebs largely joined Opimius, or stood by in the forum and did nothing, is not at all surprising. Nor should we attribute this to some turning-point in Gracchus' career--from the very beginning Gracchus favored the rural voters and allies.