The problem I see with Santorum/Gingrich/Paul as a running mate is that the issue it is designed to solve (healing schisms within the Republican party) aren't the ones that are causing Romney the worst issues in swing states against Obama. Gingrich/Santorum supporters, largely the white-evangelicals, are not going to vote for Obama, and are likely to vote against Obama for whichever politician the GOP fields (these are the people who, when polled, tend to have a greater than majority belief that the President is a Kenyan socialist Muslim). Paul supporters may widen Romney's base within the GOP (though it is hard to see why Paul supporting Reps would vote for Obama, it is always true they could go to the Libertarians or some other third party), but he is disastrous for the swing votes Romney needs to pick up in the general election, and I'm not sure a Paul VP is enough to draw Dems who may be unsatisfied with Obama's civil liberties record.
Salon had an interesting article about this the other day:
http://www.salon.com/2012/04/04/mitt_romneys_fooling_himself_about_women/
The latest Gallup poll shows how bad things have gotten for the former Massachusetts moderate. He now trails President Obama in 12 swing states, largely because of the defection of independent women. Female independents now back Obama 51 to 37 percent – and that’s a 19-point swing just since the end of 2011, when they preferred Romney. But here’s a little data point for Haley: Only two in 10 independent women polled by Gallup even knew Romney’s stance on contraception. Those who did disagreed with Romney 2-1. More independent women – four in 10 – knew Obama’s contraception position, and they were divided about evenly. Still, 60 percent didn’t know either candidate’s stance. That suggests contraception matters, but it’s not the only thing driving independent women away from Romney and the GOP. But that’s not good news for Republicans, either.Ayotte is right: Women care about the economy. And that’s hurting Romney in two ways. First, the economy is getting better, which always helps the incumbent, with both genders. But also, women have been more reliable Democratic voters since the age of Ronald Reagan largely because they support safety net programs and they dislike candidates who pledge to eviscerate them. Paul Ryan’s budget, which Romney thinks is “marvelous,” shreds the safety net into lint, and it will turn off at least as many women as the GOP’s contraception policies.
If the biggest issue Romney is facing in November is female independents (as male independents might as well just be called Republicans), Santorum/Gingrich/Paul are terrible choices. The first two for obvious personal and fairly clear misogynist flaws, Paul more for his actual policy opinions. Whether you think they are more constitutional or not, Paul's policies are not what women vote for. They don't want to risk the safety net, they don't want to renegotiate Roe v Wade or Civil Rights, they don't want to think about their kids suffering in some private school system or whatever.
I don't know the panacea, and I'm sure Romney has far more educated advisors than myself, but I can't imagine picking one of his primary opponents as a running mate is going to help him in the demographics he needs to win a general election. I'd actually argue these rumors are designed specifically to garner more support for Romney during the primaries. Let slip that he is considering Santorum/Gingrich as a running mate, suddenly evangelicals may be less skeptical of his Mormonism and Romney receives more delegates in highly contested primary states. Let slip it might be Paul, and suddenly the rabid libertarians [sic] in the GOP may see Romney as the superior choice to Santorum/Gingrich, and more votes come in for Romney.
I can't see any of those options as realistically being anything more than political suicide for a general election though... (however, if Obama decides to run against the Supreme Court, as he has insinuated recently, it may not matter who the GOP nominates anyways)