Henry Adams' History of the United States of America During the First Administration of Thomas Jefferson explains the developments e.g. in the following excerpt (pp. 80). In short, it seems that Jefferson was "just" being pragmatic in a matter that he deemed important for the nation and for his party.
... the President, according to his letters, had little hope of quick
success in the purchase of territory [because it would need express
sanction from the States in the shape of an amendment to the
Constitution.] His plan was to "palliate and endure", unless France
should force a war upon him; the constitutional question could wait,
and it was accordingly laid aside ...
Already Jefferson had ordered his ministers at Paris to buy [the
Floridas and New Orleans], although he thought the Constitution gave
him no power to do so ...
Jefferson foresaw and accepted the consequences if the necessity; he
repeatedly referred to them and deprecated them in his letters; but
the territory was a vital object, and success there would, as he
pointed out, secure forever the triumph of his party even in New
[He wrote in a letter] "I believe we may consider the mass of the
States south and west of Connecticut and Massachusetts as now a
consolidated body of Republicanism ... If we can settle happily the
difficulties of the Mississippi, I think we may promise ourselves
smooth seas during out time."
[The "Chronicle" of June 30, 1803] contained a single headline ... "Louisiana ceded to the United States!" ... The President's first thought was of the Constitution. Without delay he drew up an amendment, which he sent at once to his Cabinet.
Stephen Ambrose (in Undaunted Courage: Meriwether Lewis, Thomas Jefferson, and the Opening of the American West) recommends Henry Adams as the primary source:
Napoleon's decision to sell not just New Orleans but all of Louisiana , and the negotiations that followed, and that Jefferson waived his strict constructionist views in order to make the purchase, is a dramatic and well-known story. It is best described by Henry Adams in [ibid.]