Mexico had a hard time getting anyone to settle in Texas (and everywhere else in northern Mexico, for that matter), which is why Americans were invited there in the first place. So, if the offer is never extended in the first place, Texas will be at a lower population for a lot longer. For that matter, you might have Americans moving over the border all on their own and settling there; the border was poorly monitored by either side. Texas and the rest of northern Mexico will be coveted by a growing USA, particular TX... it was superb and plentiful land in the east half. I think you'd still have a Mexican War here, but it would be a harder job for the USA, not having TX to start out of... not sure how that would go..