However, Samuel Demeulemeester has recently written to me with several example from the same time frame, but slightly earlier. Jeff Busby was at the time a Congressman from Mississippi. Willford King was a professor of economics at New York University, and a Fellow of the American Statistical Association. Irving Fisher is in the story, too. In short, the metaphor was not a one-off comment in 1935, but was demonstrably familiar to policy-makers and academics at this time. What follows is from Demeulemeester, with his permission (for ease of reading, I have not inserted additional indenting or quotation marks to his email):
I just came across your post of July 30, 2015, “Pushing on a String: An Origin Story”, in which you suggest that this metaphor might first have been used by Representative T. A. Goldsborough during hearings held on March 18, 1935.
Goldsborough actually seems to have gotten this metaphor from Willford King of New York University, who used it during hearings before a subcommittee (presided by Goldsborough) of the Committee on Banking and Currency, House of Representatives, on January 30, 1934. King had himself heard it from “somebody” else:
Mr. BUSBY. Therefore, I think it is more essential we go to the question of dealing with both the up and down amount of bank money that may be issued so as to control it.
Mr. KING. You can prevent overissuance of this bank-deposit currency, but it is very hard to prevent underissuance of the same thing. As somebody said, you can push on a string but it doesn’t produce very good results.
Mr. BUSBY. That is exactly what I have in mind, and I want to see some kind of scheme worked out where we are pushing on the string and you can see some effect on the other end of the string.
(See here, p. 71)This Mr. Busby would himself use the metaphor in an exchange with Irving Fisher two days later, on February 1, 1934, before the same subcommittee:
Mr. BUSBY. As Dr. King said yesterday, you can pull on a string and feel the effect of it. Therefore, you can pull down the fixed media of exchange, but you can’t push it up, just as you can push on a string and feel no effect at the other end. So in adverse times when property prices are falling the only remedy I see to get efficiency out of the arrangement is for the Government to step in and supply where this by-product of the banks' activities is wiped out.And Fisher himself would use a variation of the “pushing on a string” metaphor in the following passage of his book 100% Money (1935):
(Ibid., p. 85)
Such must often be our predicament so long as we have a system under which our circulating medium is a by-product of private debt. The time when nobody wants to go into debt is the very time when we most need money and so most hope that somebody will kindly accommodate us by going into debt. Few will do so, despite all the official urging and coaxing and despite the low rates of interest. It is a case of leading a horse to water without being able to make him drink. Or it is like “pushing on the lines” to make the horse go.
(1935, 1st ed., p. 94;  1936, 2nd ed., p. 105; this passage already appeared in a 1934 draft version of the book)
_______________________As Demeulemeester points out in a follow-up email: `By the way, King's statement, as I re-read it, only says that he did not originate the phrase "you can push on a string but it doesn't produce very good results'. This leaves open the possibility that he was the first to apply this metaphor to monetary policy."