Bill Clinton, while popular, hasn't had the same amount of gravitas in that respect, though that may have to do with him still being alive and probably has to do with his reputation as a moderate.
The hate reigned down on neoliberals is why Republicans will never get over Reagan. While technically neoliberal, he sported the tricorn hat of ancient conservatism to rally his base. The founding fathers rhetoric didn't really jive with Laffer Curve theory and expanding federal spending, but conservatives didn't care. They saw what they wanted to see, and they still see it today.
Besides the liberal Democrat obsession with maintaining the racial higher ground, I suspect the polarization of US politics is why the DNC chose Barack Obama, rather than Clinton. He speaks to the left wing base, which is a good thing for Democrats.........in theory