This is an example of how to resolve RP conflicts on a person-to-person level for old-school D&D. I really like it, but it's a bit pricey for what amounts to a sub-system of a game, so I'll sketch out the basic idea:
1) You have a basic reaction, between 2 and 12, which you can either roll for on 2d6 or assign. 2 represents open hostility, 12 represents complete agreement. A character's Charisma bonus modifies this base roll, so someone with a +1 will never get an automatic failure.
2) This number also represents the number of chances you have to win an NPC over to your point of view. You have a number of actions you can take, including Threaten, Flatter, Bribe, Offer Help, Request Help, etc.
3) Some of these are automatic successes based on the NPC (the GM determines this), some are automatic failures, but most require a dice roll and possibly some other kind of action. 8+ on 2d6 is the most common level, but you might instead assign a DC 15 on a d20 or whatnot.
4) Success brings the reaction level up one point, and may have other bonuses based on the tactic and the NCP. Failure drops the reaction level down one point.
5) At any point where the reaction reaches 2 (complete hostility) or 12 (absolute acceptance, friendliness), the RP conflict ends and the NPC fights, helps, ignores, or flees from the PCs, or does whatever is most reasonable for the situation.
6) Otherwise, the RP conflict ends when the number of actions runs out. NPCs have 5 levels of reaction at this point: 2 (complete hostility), 3-5 (dislike, distrust), 6-8 (neutrality), 9-11 (favorable opinion), and 12 (complete acceptance).
I suspect this can be applied to public oration as well, although the specific actions might be different: tell a story, praise an individual, condemn a group, argue a fact point-by-point, use poetic diction and flowery metaphors, etc. Also, see my reply to /u/VDRawr's comment: you don't base the response on how a player says something, you base it on what their character says. This is at a high level, pertaining to their intent, and not at the level of specific words or even sentences.