While I agree with you that the winning party must hold together the base, I disagree about moderates and Obama. He won the self identified moderate vote by 60% to 40%, while Romney won over the independents, but still managed to lose the election, for obviously a number of reasons. People are kicking around Paul's name these days, and he's made it pretty obvious he'll be in the race. But as you say, he's walking a tightrope with issues. You simply can't be all things to all people.
If Bush does jump in, in spite of his mom's wishes, I would suggest it'll be in part to offer an alternative to Christie, who's got problems of his own.
Obama won the moderates, but he did not do so by APPEALING TO the moderates. He ran as a leftist, trusting that moderates would come along because of his authenticity. Given the polarization and marketing savvy of the electorate these days, there is no longer a significant "center." The great American middle class is disappearing. To win a plurality, a candidate has to stitch together a unique combination of constituency groups. The failures of McCain and Romney strongly suggest that the traditional coalition the GOP has always counted on can no longer win a national election. New votes have to come from somewhere.
Some people think we should pander for the Hispanic vote. The trouble with this strategy is that it is a quest for a minority within a minority. The GOP is never going to be popular with a majority of Hispanics.
On the other hand, there are enough swing votes out there in the anti-establishment libertarian movement that, if it could be combined with the traditional GOP-leaning core of the party, can swing the party back into a majority. And it's built on a more solid foundation, standing for personal liberty as opposed to handouts. And since it is youthful, it could be sustainable.
Now, many will claim that there simply is not enough common ground between the religious right and libertarians. But I think there might be so long as everyone feels their own freedom is at stake. Religious people feel they are under attack. Gays and lesbians feel they are under attack. Recreational drug users feel they are under attack. Small businessmen feel they are under attack. Doctors, lawyers, nurses, Realtors and especially working men and women feel they are under attack. If someone just came along and said "Live and Let Live" and was trusted, and not pressed too much on the details of what that might mean, it could win a national election.
Personally, I think Romney could be president today had he chosen Rand Paul as his running mate. Paul would have appealed to voters in OPapaDoc's center: the young, energetic, pierced and tatoo'd crowd that just wants its pot and Internet, and doesn't want to be hassled. Instead, he picked the safe choice, Paul Ryan, who could not even deliver Wisconsin.
You can't just keep thinking the same old way and expect a different result.