A question from commenter SNF: “Do you think that Rand Paul's comments on the Civil Rights Act would hurt him in a general election, assuming that he won the nomination? What about Jeb Bush's last name? Do you think being a Bush would hurt him in a general election?”
The big picture answer is that (non-incumbent) candidates don’t matter very much in presidential elections. By November 2016, Republicans will have plenty of reasons to rally behind the Republican candidate and to hate the Democrat, and vice-versa. And most of us wind up voting as partisans, even if we think of ourselves as independents. The big exception is when an incumbent runs. Then, approval or disapproval of the president is strong enough to shake a lot of partisans out of their usual voting habits. But the effect is smaller when it’s just a would-be successor from the same party as the incumbent president (though as John McCain could tell you, it still matters if the outgoing president from your party is highly unpopular).
That said, the biggest effects that candidate can have (short of some extraordinary scandal or incompetence) is that there is a penalty for perception of ideological extremism. It’s not large (maybe a few percentage points in cases such as Barry Goldwater in 1964 and George McGovern in 1972), but it can matter. Paul probably would be seen as an extremist, but I don’t know how much of that has to do with his controversial comments about the Civil Rights Act. (In 2010, he suggested the law was inimical to libertarian principles. However, in a speech at Howard University last year, he said his support for civil rights has "never wavered.")
This also suggests that Jeb Bush wouldn’t be hurt by his family’s less-than-stellar presidential record. But “suggests” is as far as I would go. We have a limited number of presidential elections to look at, and the sample is even smaller if we’re looking only at modern conditions and availability of data. Republicans don't want an election that is focused on comparing the Bush years to the Clinton years. And for at least some voters, a Bush on the ballot (especially if there’s a Clinton, too) might cause them to make that comparison. My guess is the effect would be tiny or non-existent, but there’s never been a similar situation, so there’s some unknown here.
In any case, any advantage Bush might have for seeming more “presidential” thanks to his family background wouldn’t hold up long. Right now, Marco Rubio and Bobby Jindal and the rest might not seem very presidential, but neither did Barack Obama, Bill Clinton, or probably George W. Bush at this stage. The general-election campaign, including the national conventions, is designed (among other things) to convince wavering potential voters that their candidate is a plausible president, and campaigns perform that function extremely efficiently. Which is one of the reasons, to circle back around, most traits of most nominees just don’t matter very much in November.
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