Do you think eight years is more likely than four? She won't be challenged from within her own party because would-be challengers would have to fear getting Vince Fostered. But the Republicans will probably recover by then (and probably by 2018 in fact), and Hillary's popularity may not increase after she takes office. There are abundant* potential Republican nominees who are more popular than Hillary (even if nobody yet knows who they are).
People very often exaggerate the rumors of a major party's demise. I remember a bet between smart people in 2008 (I think Tyler Cowen was involved in some way) about whether the Republicans would take control of the White House or either house of congress within 20 years or something. It's hard to remember now because of hindsight bias, but things looked really bleak for the Republicans at the time. They had, after all, recently nominated Sarah Palin as their candidate for Vice President. That was a continuing punchline in itself, but it also signaled how the Tea Party wing was going to ruin the party's chances in national elections. Anyway, the bet was lost after just two years when the Republicans won the House in 2010 and proceeded to gerrymander their way into keeping it for the foreseeable future. They've also got the Senate (at least for now) and the majority of state governorships -- and they may have had a real shot at the White House this go-around if they'd put up a different nominee.
I'm just saying that political parties often look like they have bleak prospects for the foreseeable future, but tend to recover and compete for political prominence again a lot faster than people generally expect. I don't see why that can't happen between now and 2020 (though, to be sure, there is a lot of work to do in jettisoning certain planks in their platform and forming new coalitions that involve demographic groups beyond just old white males without college degrees).
It may turn out that Clinton is a more popular (and more competent) President than she was a campaigner. That would be nice. But it's also possible, and perhaps probable, that she'll never enjoy widespread popularity, and that Generic Republican Untainted By Trump will be a decent favorite in 2020.
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			*Not a Chris Christie joke.