Seems according to this document* (Appendix A, Note 1) that Kennedy thought the only limit to the size of the deficit and debt was inflation. To be exact, the conversation between Kennedy and James Tobin went as follows.
Kennedy: “Is there any economic limit to the deficit? I know of course about the political limits. People say you can’t increase the national debt too fast or too much. We’re always answering that the debt isn’t growing relative to national income. But is there any economic limit on the size of the debt in relation to national income? There isn’t, is there? That’s just a political answer, isn’t it? Well, what is the limit?”
Tobin then says (describing the exchange of views) “I said the only limit is really inflation. He grabbed at that.”
Kennedy then says, “That’s right, isn’t it? The deficit can be any size, the debt can be any size, provided they don’t cause inflation. Everything else is just talk.”
The only criticism I’d make of Kenndy’s summary of the debt and deficit there (and indeed, this is a criticism of MMT as well) is that there is actually another limit to the size of the debt, which is that if the deficit is larger than is needed to bring full employment, with a consequent excessive debt piling up in consequence, government and central bank will be forced to raise interest rates unnecessarily so as to damp down the excess demand that stems from the private sector finding itself in possession of more government debt than it wants, and trying to spend away that excess.
Incidentally, those holding government debt cannot of course spend their debt directly on consumer goods or whatever, but they can wait till their particular tranche of debt reaches maturity and then spend the dollars they get at that point rather than reinvest the dollars in more debt.
And finally, I am indebted to “Matthew B” (a Bloomberg journalist) who dug up and publicised the above points about Kennedy.
*Council of Economic AdvisersOral History Interview –JFK#1,08/1/1964