Although often quoted, it seems Dirksen never actually said this. The Dirksen Congressional Research Center made an extensive search https://web.archive.org/web/20140127115225/http://www.dirksencenter.org:80/print_emd_billionhere.htm when fully 25% of enquiries to them were about the quotation. They could find Dirksen did say "a billion here, a billion there", and things close to that, but not the "pretty soon you're talking real money" part. They had one gentleman report to them he had asked Dirksen about it on an airplane trip and received the reply: "Oh, I never said that. A newspaper fella misquoted me once, and I thought it sounded so good that I never bothered to deny it."
The Yale Book of Quotations cites a similar statement in The New York Times on Jan. 10, 1938: "Well, now, about this new budget. It’s a billion here and a billion there, and by and by it begins to mount up into money." https://books.google.com/books?id=ck6bXqt5shkC&lpg=PP1&dq=%22fred%20r.%20shapiro%22%20yale%20book%20of%20quotations&pg=PA206#v=onepage&q=%22everett%20m.%20dirksen%22&f=false
Misattributed