I think it is a bit more than 35 % but that is quibbling over the margins. The problem is not with what percent of population supports what, but with the institutional framework of the US political system. The US is for all practical purposes a single party state where anything left of the center has virtually zero presence in the key political institutions. So it does not really matter what people think if that thought has no correspondence in institutional reality.
A third? Half? Two thirds? Of the population may be moderate or liberal - but then so what? How are they going to translate that preference into political influence if there are no institutions already in place willing and able to implement that popular will. In the same vein, a substantial share of the Iranian population may favor European style liberalism but that does not mean a shit since there are no political institutions that can implement such a program. And there are no such institutions because in both countries the fundamentalist factions eradicated all effective opposition.
This should not be construed as an opinion that there are no differences between the two parties in the US. There are. But these differences are confined with the rather narrow political spectrum and will not leave that straitjacket, the popular will (if any) notwithstanding, because the ruling oligarchy will not let that happen, by hook, crook or force if necessary. I don't think that Chuk0's Molotov's cocktail will make much impact on the National Guard, let alone the US Army.
Wojtek