That depends on why the Purchase isn't made.
The offer isn't made?
Somebody else gets in first?
The USA is still under the 'Articles of Confederation', rather than the later OTL constittuion, and something about that situation makes the purchase impossible?
The USA decides that it simply can't afford the purchase?
The USA decides that (as some people suggested, IIRC, at the time...) acquiring new lands by purchase like that -- rather than through their inhabitants organising as states and then asking for admission into the union -- would be unconstitutional?