Are you sure the meaning of the word 'little' in the first phrase was 'not many'?
A person may have 'little things to do', but it means he/she has a few or many little (=not big) things to do.
When describing countable nouns, 'little' can only denote size, not quantity.
(btw. with non-countable nouns it cannot denote size, e.g. 'little milk')
IMHO, off course