It’s possible to persuade these lukewarm voters to turn on him; you can see it begin to happen in the polling data when his party pursues unpopular policies (the Obamacare repeal push) or when his personal chaos seems to produce a real political breakdown (the government shutdown) or when his bigotry seems linked to some real-world horror (as with Charlottesville). But when a feeling of stability returns, when there isn’t a cascade toward economic debacle, foreign-policy catastrophe or late-1960s civil strife, these voters drift back toward mixed feelings, lukewarm support, dislike leavened by skepticism about removing Trump via impeachment rather than the 2020 vote.

Which is why, to return to the initial hypothesis, it mattered that the impeachment debate began at the same time that Trump was stumbling badly on foreign policy with Turkey and the Kurds; it gave some of these voters (and the swing-state Republican senators who represent them) a feeling that maybe this time everything was going to fall apart at once, that Trump’s incompetence would blow up the Middle East at the same time that his scandals multiplied.

Then the pattern in polling since — the dip in his approval rating giving way to a tiny upswing, support for impeachment peaking and then declining just a bit — might not reflect some dramatic failure by Democrats to make the case or some dramatic success for the Trumpian defense. Instead, it might just reflect the fact that the situation in Syria seems to have temporarily stabilized, the economy is fine and there are voters who will support removing a president when the world seems to be falling apart, but if it’s not, then not.