The Inherent Incompatability of Morgoth and Sauron

[Zigûr]

Originally Posted by Sarumian

When he found that other Valar were reluctant to take reigns in ME, could he treat that attitude as a confirmation of their failure? May be he even had a hope that taking responsibility for the affairs of ME and ordering he could deserve Eru's respect in the future?

If we imagine Sauron's worldview as being that the worthiest cause and highest moral responsibility was the implementation and maintenance of order then I agree that we could read Sauron as seeing the Valar as equivalent failures for their refusal to bring order to Middle-earth, instead in fact leaving Men to the depredations of Morgoth's scattered servants.
As for Eru's respect, however, I don't think that by this point (especially following Morgoth's defeat) Sauron was devoted to any being but himself, and any cause but his own obsession with order. I think Eru would be too abstracted and uninvolved to hold any further interest to him. He might even represent everything Sauron was opposed to, which is to say letting things take their natural course (and although he must not have realised it, still intervening, but subtly). The only inconsistency is the destruction of Númenor, but this seemed to Sauron, apparently, to be Eru's last act of dismissal towards his "failed" creation. Sauron judged all decisions, in Gandalf's words, "according to his wisdom," which is to say what he would have done in the same situation, so we shouldn't be surprised at Sauron's ability to rule Eru out of his equations, something only a mind as corrupt as his could do.

Originally Posted by Nikkolas

The Valar did nothing but fail. They brought the Firstborn to Valinor, leaving Men all alone to be brainwashed by Morgoth, they allowed most of the Noldor to leave Valinor and get themselves slaughtered, and when they finally did take action most of the greatest Elves and Men ever were already dead and what they all were trying to save was destroyed.

Interestingly there are responses to this in "Myths Transformed" where Professor Tolkien describes Manwë as "the spirit of greatest wisdom and prudence in Arda" with the argument that "the heroic Noldor were the best possible weapon to keep Morgoth at bay, virtually beseiged, and at any rate fully occupied, on the northern fringe of Middle-earth, without provoking him to a frenzy of nihilistic destruction."
I think the Valar definitely made mistakes (bringing the Eldar to Aman may have been one of them; Ulmo thought so) and as a result they were forced to compromise. The only alternative (direct action) might have risked Arda itself being destroyed.