It seems to me that as the Republican primaries progress, the surviving candidates will be probing one another's weaknesses looking for ways to climb over one another. This is what's happened in recent presidential elections. Obviously, this is part of the process to reach the presidency. And because of its uncertainty, it's always a dangerous game, whether played by Republicans or Democrats.
Clearly, Governor Bush's family name will work against him. Even Republicans acknowledge this; why else didn't they invite President George W. Bush to speak at their conventions? Given that Governor Bush has availed himself of the advice of the neocons that gave us Iraq, Katrina and the catastrophic financial collapse, (to name only a few of the mistakes of President Bush's disastrous two terms), those are among the many failures that could be used by the other Republicans, especially the unrestrained Donald Trump, to attack and smear Governor Bush, weakening him. Obviously, those weapons would work for our side as well, should Governor Bush become the Republican nominee.
It has occurred to me that Governor Bush doesn't seem to have the fire in the belly to be president. It feels like it's expected that he's next in line, perhaps because of family pressure. His mistakes are amateurish and his positions are either outside the majority view of our country or poorly articulated featuring mis-spoken statements and many explanations where none should be needed. Since Mr. Trump is (presumably) unelectable, I'm much more concerned about Governor Walker, (maybe with Carly Fiorina as Veep?), since he has the Koch's support supplemented by the mainstream of the Republican party.