I don't think Keynesians advocate "spending more than you have" forever. The thrust, as a I understand it, of their arguments is that deficit spending can be useful in getting out of a downturn and can have beneficial aspects. Of course, if done improperly, it can have bad effects.
I don't think Keynesians advocate "spending more than you have" forever.
As you indicate, Keynes by-the-book does not. He would have us actually save during booms, so that we can pump up the economy in the busts.
However, in practice, those in power who follow Keynes seem to be doing so not because of any belief in the economics, but because it justifies their wish to buy greater power by wielding more money. Thus, they don't follow the invest-when-booming part of the model. The result is that the government spending is at best balanced, and much more often it's in deficit.