Captain David Livermore believes that the much-derided boss is still the man for the job, despite recent opinion polls suggesting that an overwhelming number of supporters want to see Tuttle removed from the hot seat - even if The Lions somehow manage to stay up.
The team have only won four games under the Tuttle but in an interview with the South London Press, Livermore revealed that the players all want him to stay.
"I don't think any other manager could do any more, or as good a job, than Tutts has done," said the captain.
"He's been thrown in at the deep end, under difficult circumstances where he's not been able to get the players in he wanted.
"We knew he wanted to improve the squad in January and it didn't really happen. But he's still kept us fighting, and done it with a lot of kids, and without key players who have got injured."
Many Millwall fans will feel little sympathy with the manager over the lack of transfers since he took charge.
Despite signing winger Lloyd Dyer and striker Berry Powel, Tuttle decided to play favourites and used both players sparingly - which resulted in Dyer cutting his stay short and Powel threatening to do the same after claiming that he'd been frozen out by the manager.
And certain members of the board have even laid the blame for the lack of signings at the feet of Tuttle, claiming that he didn't make his transfer requirements clear enough at the time.
But Livermore still feels that he is the best man for the job, and after a spell of four managers in just eleven months, the club should look to gaining some stability rather than rock the boat further.
"We've had seven managers in seven years and I don't think another manager change would help the situation," he told the SLP.
"We need to give a manager a fair go at the job, and build up the club in the right manner. Not keep chopping and changing.
"What is needed is stability, and because Tutts has the players' backing, him staying on after the end of the season would mean we'd have some."
"Us players read the papers, and see stories about Tutts perhaps not being in charge next season. But we want to know as soon as possible who will be in charge next season and we are hoping it's Tutts. If not, we want to know who else it could be, and what sort of players would be brought in."