I have yet to encounter anyone in the flesh who cares in a major way, Left or Right.
I suspect the Dem strategists think this is some kind of a ticket to undermine Trump and the GOP with the press (Like it was even possible to make them more anti-Trump). And there are also factions of both the GOP and Dems who are hostile to the Saudis 24/7 who want to seize the chance to pursue that agenda.