In "The Devil and Tom Walker," what is the romantic idea that is most reflected in the story?

Since the story, written by Irving, is listed by some texts as one of the American Romantic era stories, I assume you mean "romantic idea" in the sense of the period of literature, not in the sense of amorous love between two people.  The inspiration for the story, according to the e-notes introduction, might have come from the German romantic writer, Faust.  His story though had the one who made the pact with the devil winning love as well as money.  Irving's character, Tom Walker, only wants money.  Romance-era writers dealt with possibilities, dreams, magic, and other such ideas.  This story has all three of those: Tom Walker dreams of being rich and the devil, through his magic, makes that possible.