We can't even agree on reality or what a "fact" is for Christ's sake. How is one suppose to unite the country with a clear mandate absent a national crisis in this kind of environment? It does not happen.
Wouldn't that also imply that, if a national crisis occurred, we couldn't even agree with our interpretation of it? For example, if another 9/11 type event occurred, then we'd have divisions over the proper response (military vs. diplomatic, immigration restrictions vs. their opposition, etc...), the cause ("they hate us for our freedom" vs. "we provoked them by being in their lands"), and perhaps even the details of the event (inside job/conspiracy theory vs. acceptance of government/news reports). That similar division could be applied to practically any crisis, whether it's terrorism, natural disaster, economic crisis, or whatever.
So, no, there is no Democrat, Republican, or anyone that could unite Americans.