Final answer:
Roosevelt's statement contains a pun due to the double meaning of 'nothing,' but the correct answer from the given options is an idiom, as it's a phrase with a figurative meaning.
Step-by-step explanation:
The statement by Roosevelt, "It is said that nothing is impossible; but there are lots of people doing nothing every day" is best categorized as a pun because a phrase in the statement has two meanings. Specifically, the word "nothing" is used both to denote the concept of "impossibility" and the act of "not engaging in any activity". However, this type of wordplay is not listed among the provided options. Thus, the closest option and the correct answer in this list would be idiom (4), as it is a phrase that has a figurative meaning different from its literal meaning, and here "doing nothing" can be interpreted as living without achieving or engaging significantly, which is a figurative use of the phrase.