"Wasteful government spending" is a propaganda meme used to justify austerity, when it usually is just a dog-whistle for "screw PBS/NASA/the poor". Notice how the "waste" never seems to be found in the traditional crony/bankster favorites like our huge military or anything resembling a subsidy for Wall St. Removing "waste" sounds good, but you have to make sure it's actually "waste" being removed, and not the usual political targets.

The real problem with austerity is that it makes debt bigger by shrinking the underlying GDP, and a fallacy of composition where individually rational actions (e.g. cutting your personal expenses so you can pay down your debt) doesn't work if we all do it at the same time. The solution often is some variant of "grow your way out of recession". It's not a great solution, but it's probably the least-worst plan. This may or may not involve make-work programs; an "anti-austerity" plan may simply be a plan that stops ruining the GDP with cuts.

(trickle-down the opposite idea, I'm not sure why you associate it with anti-austerity)

Never mind Krugman - I highly recommend Mark Blyth's (prof. econ. Brown Uni) discussion of the topic ( https://www.youtube.com/watch?v=B6vV8_uQmxs#t=674 - the main lecture starts after a boring introduction at ~12min). While this particular lecture is focusing on the situation in the EU, Blyth covers a lot of general econ topics and spends a lot of time on the history of austerity and what it does to an economy.