what is the latest in the season a player might come back and say "I might be interested after all by I want more money?"

If it makes any difference, in this case I want the player, not the type D pick, but this is a "probably won't sign" momma's boy.

Impossible to say. Unexpected things I've seen:

1/ A "probably won't sign" momma's boy sign the first offer, same as a "will sign for slot money" guy...

2/ A "questionable" guy decline the first offer and then mysteriously accept it a few days later with NO increase...

3/ A "considering another sport" guy decline my offer multiple (I can't remember how many) times and then accept an increase with only a few days left in the playoffs...

About the only thing you can count on is a "slot money" guy will sign for slot money. Everything else, I don't know if anyone knows the odds.