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She set a tone at the very start when she walked right into his space to shake his hand and made him almost pull back into himself in response. She was in charge and never stopped being in charge.
Harris also managed what neither Joe Biden nor Hillary Clinton nor any of the 2016 Republicans managed to do which is successfully bait Donald Trump and get under his skin. Within a few minutes Trump was visibly angry and not in a way that empowered him but in a way that made him lose focus, go down rabbit holes and generally go off onto damaging tangents. Spittle anger, not righteous anger, shall we say.
She was only the VP, though. Her job is to do the things the President lets her do, and break up fights in the Senate. VPs simply don’t do that much. She could (and did) bring out the accomplishments of the Biden administration, but that just called attention to the fact that Biden had to drop out, so she could only do it sparingly.
Also, Donald “I have the concept of a plan, I’m not president” Trump probably shouldn’t be pushing that angle too hard
I know the below doesn’t quite work since Biden dropped out before 8y but doesn’t it benefit the party for the president to give some higher profile jobs to the VP so the VP can campaign on those after their 8 year run? Maybe they wait for the 2nd term to be more beneficial, but it’d seem like a good idea for both terms in case something like this happens.