"Had we but world enough and time/This coyness, Lady, were no crime" is the beginning of "To His Coy Mistress" by Andrew Marvell, who died about a century and a half before Whitman was born. There is no good reason why the Secretary of State should have a literary education, but it's odd to see her apparently faking one. If we assume the line was provided by a speech writer, it's odder still that he wouldn't have checked the source of the quote.
All of which reflects one of the many things that bothers me about our educational system. Considerable parts of it appear designed to teach people to pretend to intellectual tastes and knowledge that they do not possess and that there is no good reason why they should possess.
I will now wait for some Whitman enthusiast to find the line echoed somewhere in Whitman, and accuse me of lacking a literary education.