Is suffering always present? I'm reading Thich Nhat Hanh's "The heart of the Buddhist teaching". When discussing the three dharma seals he talks about misconceptions of suffering. He says that teachings where suffering is considered a basic element of reality are wrong:


  But sometimes only Two Dharma Seals are taught - suffering and
  nirvana. .... But suffering is not a basic element of existence. It is
  a feeling. When we insist on something that is impermanent and without
  self being permanent and having a self, we suffer. The Buddha taught
  that when suffering is present, we have to identify it and take the
  necessary steps to transform it. He did not teach that suffering is
  always present.


This makes sense to me intuitively How do the different schools, i.e. TNH as well as those opposing, justify their position? What do they use as their reference?

I have read this Q/A here however I am more interested in the references and how the different ideas are defended. The Q/A linked seems to be more opinion based, which is fine of course.
I think that the second noble truth says that suffering co-arises with craving -- and the third noble truth says that cessation (of craving and suffering) happens.

It's being called "pervasive", I think, comes from the tilakkhaṇa -- i.e.:


  
  sabbe saṅkhārā aniccā — "all saṅkhāras (conditioned things) are impermanent"
  sabbe saṅkhārā dukkhā — "all saṅkhāras are unsatisfactory"
  sabbe dhammā anattā — "all dharmas (conditioned or unconditioned things) are not self"
  


Note that it's "sabbe saṅkhārā" i.e. "all conditioned things" -- not "all dhammas" -- that are unsatsifactory.

Also note that "dukkhā" there is translated "unsatisfactory" not "suffering" -- i.e. the things themselves are unsatisfactory and impermanent.

Whereas "suffering" (with is another translation of "dukkhā", a context in which "dukkhā" is used) might be slightly different -- i.e. an aspect of consciousness which co-arises with craving and attachment -- i.e. craving and attaching to sankharas which are unsatisfactory and impermanent.