the subflooring will do the trick, but it will only get so close to the cabinet base boards.
Check for nails, set the blade, and first make sure there are no hidden dangers in the path of the kerf.
If you wanted to still get closer than the circular saw would do, then add a new tool to your arsenal and get a roto-zip with the cut off attachment and then adjust the blade again and you can snug up to that base easily.
BTW, if you don't have this tool, this is one excellent time to get one. Your significant other will surely understand, and the circumstances definatley warrant it.
Roto-zip sells for $80 and the attachment is another $40. You'll love it.