Nah, we can do pretty well with just wind and solar.
The practical difficulty with using renewables effectively is that you need to be able to either store large amounts of energy for later use, or trade power across long distances. We (by which I mean "in the U.S." but for other developed countries it's pretty much the same) could buy solar power from Kenya, Australia, Algeria, or similar places to get us through the night if we had high-capacity transcontinental HVDC lines running to those places. That's a major infrastructure project that would cost a lot of money, but I expect it's probably worth it.
(We can even mitigate the risk of the power lines being temporarily disabled by keeping the fossil fuel plants on standby and just not using them except as an emergency backup.)
Another option is to just build batteries on an unheard-of scale. Lithium iron phosphate cells might do the job -- being free of cobalt an nickel, the only other major bottleneck resource would be lithium. I'm not sure how practical it is to build the kinds of gigantic battery packs that would be needed to provide, say, an 18-hour backup power supply for the entire U.S., but it's probably less cells in total than we'd need to electrify our current fleet of gas-powered cars.
edit: to clarify, I'm not particularly opposed to nuclear. I just don't think it's the only option at this point.