That doesn't make a difference - regardless of where you put the opening quote, make gets the string "CFLAGS=-I/path/with spaces" as argv[1]. The quotes do help, as otherwise it gets split up into multiple arguments to make.
But actually, I was wrong - GNU make passes strings to execute to the shell, so you can use nested quotes: CFLAGS='"-I/path/with/spaces"'. Not sure why I thought differently. The shell itself doesn't work this way, though: when it splits a variable into multiple arguments, it just splits by spaces rather than doing any fancier processing. So there are issues with shell scripts.
But actually, I was wrong - GNU make passes strings to execute to the shell, so you can use nested quotes: CFLAGS='"-I/path/with/spaces"'. Not sure why I thought differently. The shell itself doesn't work this way, though: when it splits a variable into multiple arguments, it just splits by spaces rather than doing any fancier processing. So there are issues with shell scripts.