I have been negotiating for most of my professional life. The idea you will get some concessions on the "big stuff" if you roll on the "little stuff" is idiotic. All you do is give your opposite the impression you are not willing to fight. It is not about the little battles or the big battles, you try to win them all. If a point is not important, you should not fight for it. Period. If it is important, no matter how small, you fight tooth and nail.
That is true no matter what you are negotiating, a widget contract, a car, a house, federal spending.
To believe otherwise proves you are nothing but a politician, worried about the next election.
I should never have expected otherwise.