Of US Commercial electricity use about 40% is refrigeration, cooling, heating, and ventilation which can all time shifted at least intra-day with good building practices.
10% is lighting which realistically can't - you need lights when it's dark.
15% is computers which can sort of load shift because most office computers are now laptops - with good communications systems you can tell laptops how aggressively to charge / whether to run off battery.
The rest is "other" quite a lot of which is small electronic devices like tablets and phones charging and then a grab-bag of misc. stuff.
Half of residential electricity is some kind of temperature shifting (heating, cooling, refrigeration, freezers, ventilation).
Essentially with good insulation you can get to a point where you can load shift 50%+ of your electricity consumption on an intra-day basis.
Electric car charging of course is a perfect load to match to renewables as well.
That doesn't solve the issue of inter-day fluctuations - what happens when you have a cloudy, high pressure system sitting over a substantial part of your generation for a week - but it does mean that we can go pretty far. We may have to keep more open-cycle gas around for those times which will have to be funded on a capacity basis.