Paul, the letter you mention was sent to James Madison. Jefferson had been pondering the question whether we should inherit any government obligations, whether in the form of constitutions, statutes, public debt, or private debt. Having tentatively concluded that we shouldn’t, he wrote to Madison with this idea.
In response, Madison made several observations: 1) Obligations incurred by government in one generation may well yield benefits to the next. So, for example, if the government sells bonds to finance construction of a bridge, the succeeding generation may find itself facing the previous generation’s obligation, but it will also recoup most of the benefits associated with that obligation. To insist that every obligation have a 19-year sunset would make such government programs impossible. 2) Jefferson’s 19-year term was arrived at by him at the conclusion of calculations concerning the length of a generation. Madison pointed out that generations don’t work that way: there’s never a day when one 19-year generation ends and the next begin; children are born every day, and people die every day. Thus, there’s no way to say when the 19-year term ought to start or stop. 3) Writing a constitution is not a trivial matter. Where good constitutions already exist, to throw the constitutional system into turmoil every 19 years would be foolhardy.
Madison had more to say about the idea than this. The short of it, however, is that Jefferson did not mention the idea to him again. Jefferson was prone to coming up with such notions, which he usually ran past Madison. Madison typically explained to Jefferson why they were impractical.
Part of the reason that Jefferson disliked the idea of debt passing down from one generation to the next is that the land he had received from his father-in-law was encumbered with substantial debt; he wanted to concoct a way to keep the land without paying the debt. For a full treatment of this topic, see Herbert Sloan’s fine book _Principle and Interest_. (Note that the title is a pun.)
For Jefferson-Madison exchanges, including the one that interested you, see Lance Banning’s _Jefferson & Madison: Three Conversations from the Founding_.