First of all we know the budget isn't increasing: after the news of the biggest TV deal in franchise history was signed the team President was asked if it would increase our roster budget and he said yes only to have Melnyk say that it wouldn't a few hours after.
So no, the budget isn't increasing next year and considering the TV deal added something like 40 million dollars (I think a bit less since the deal is 400 over 12 years I believe) to the team's budget and it won't do anything I wouldn't expect any increase in the short term (2-3 years) unless we make the playoffs next year and get to the second round to have a bunch of home games
The point isn't that Spezza isn't valuable, the point is that we're cash-strapped and have important players that will be needing new deals in 2015 in him, Ryan, MacArthur and Methot (probably other ones I can't think of) as of now: tough decisions need to be made to make sure we don't lose all our talent and the average of the team age needs to be considered, we're one of the youngest teams so once the current core hits it's prime Spezza most likely won't be the game breaker he is today
Spezza might simply not fit in the team's long-term plans at which point offering a long-term deal is just not a good idea, especially if you can trade him for a lot of assets which is what he's worth