Unless a much better option is made available (namely - Pop), I do not think Nate is the problem and there is no need to fire him.
These guys still pay attention to him, they still over-achieve when you factor in health - and sure, they have problems sometimes to get motivated - which makes sense given the horrendous injury bug this year. I know the players get paid handsomely for their services and as such, should be going 100% all the time, but the reality of the situation is that they are human, this has been a very, very trying year for them - and logically, like anyone else - they just can not run 100% all the time. Human beings are not machines - no matter how handsomely they are paid.
So, overall, this team still plays hard, they still win more often than they lose, even if the talent on the court is diminished or inconsistent because of age (See Bayless, Nic, Webster, Rookies) or nagging injuries (See Roy, Rudy, Nic, Aldridge).
We have seen that when Nate was not with them on that road trip after he was injured - they did not do all that well - so the idea that Monte Williams (great as he is) will just swoop in if Nate is gone and will automatically right the ship seems far fetched to me.
This team is starting to mature - only a bigger name, more respected than Nate would get them to pay more attention, rather than less, imho. Larry Brown on paper is such a name - but with his roster meddling and prima-donna personality - I do not think he is the right option. If Jackson is still healthy enough to coach, he stays in LA, if Sloan still wants to coach - he stays in Utah, the only one that might (very unlikely) become available, imho - is Pop - if the Spurs really age/lose Timmy.
So, overall - Nate is probably as good a coach out there that is available and has the respect of the team, imho.