As an exercise in teaching English, I think it can be said that JET is an abject failure. Japan has one of the lowest TOEIC scores in Asia and 23 years of JET have done nothing to improve it. As Gannon notes, the budget panel sees JET as a teaching program, not a cultural exchange project, hence its recommendations to essentially do do away with it [PDF in Japanese].
If you're a JET Alumni, you of course don't want to see the program go, but Gannon also notes that intellectuals and policy leaders are trying to convince Japan rethink its position. More importantly, Gannon writes, "For its part, the US State Department also seems to be taking the position that the JET Program makes valuable contributions to the long-term underpinnings of US-Japan relations and cutting it will be harmful."
Even if you believe the JET Program to be wasted effort in teaching English, this is where the real value in JET exists: the goodwill that Japan has bought over the years is invaluable. Teaching and cultural exchange aside, the JET Program has succeeded in creating a corps of "ambassadors" that are interested in and like Japan, and these people tend to want to continue to stay connected to Japan in some way after JET.
I know a few ex-JETS who have gone on to work at embassies in Japan, and I wonder what the ratio of people who go on to work in some Japan-related government or NPO capacity really is. If JET does get the axe, then Japan doesn't just lose a teaching program, but a valuable diplomatic tool as the State Department suggests.