Immediately the narrative is going to be about how the GOP is completely owned and ran by the Bush family and Jeb would just be the third Bush term his brother couldn't get and why they can't nominate and win with anyone not named Bush (a somewhat valid question I'll admit since the last two Republican presidents were Bushes) and basically every single thing the GOP has been trying urgently to avoid the last four years. Not to mention it'd be a liberal conspiracy theorist's dream come true and will allow them to be taken more seriously and about how the Bushes control the GOP so thoroughly they can get one of their own nominated without him even being on the ballot. There is really no response that can beat that reasoning, no "Romney and Santorum are lousy candidates" isn't enough (albeit true). A third Bush under such circumstance is a far bigger nightmare than those two despite all their baggage. I mean maybe it'd be different if Jeb ran and won the nomination fair and square (especially as this would be proof he could overcome the whole Bush name obstacle since Bush isn't too popular with the GOP base at the moment), but giving him the nomination North Korean-style really doesn't help with any misgivings they have with the name Bush they might be willing to get past.
Fun fact: the last winning GOP ticket without a Bush on it was Nixon/Agnew in 1972.