Take for example UKs wind energy input, which is charted here:
http://www.gridwatch.templar.co.uk/
(might need to zoom in a bit)
The periods of "little to no energy" take up less time than periods of "more than little". Such periods are not as your phrase suggested, the norm broken up by occasional spikes.
Total energy supply and demand is never constant or even, it varies throughout days, weeks and seasons. That variation has always had to be accommodated.
Even without more storage (hydro, battery, future??) the grid can use almost all of the input which renewables can throw at it, and use existing plants to fill in gaps.
But there will be more storage, and long range transmission lines, better solar panels, batteries and windturbines. There is no major unsolved problem here, like nuclear fusion or Mars habitation has, its just a matter of mobilizing with existing technology.
A matter which has been politically delayed for too long...