The Sox have $94 million committed to 2014, which is when Ellsbury becomes a free agent. That rises to about $107 million if Lester's option is picked up (although that option is apparently void if he finishes 1st or 2nd in Cy Young voting in any year of his current contract). They also would have to deal with the 3rd year of arbitration for Bard, Lowrie, Saltalamacchia, and Aceves (assuming all are still with the team), which will probably cost a decent chunk of money. They then have some major holes to fill from now until 2014, assuming that there are no adequate in-house candidates: RF, DH, 3B, closer, and a 5th starter.
The Sox won't spend past the luxury tax, which is somewhere aroud $165 million this season. That will undoubtedly rise, giving the Sox about $80 million that they can allocate in 2014. They need to commit that money towards 4 starting positions, probably 3-4 arbitration cases, and then Ellsbury. (Assuming no one gets hurt and needs to be replaced, and that no prospects can fill the void).
So, if the Sox need to acquire one or two marquee players between now and 2014, they should have plenty of money left over to retain Ellsbury. However, if they need to make more big signings than that, money is probably going to be stretched (some would need to be allocated to the bullpen) and make it tough to keep Ellsbury around.
I think that the payroll situation makes it pretty easy to afford Ellsbury. The only question is whether Boras' asking price will be too high (or another team were to overbid, like the Phillies did with Werth). The number of years shouldn't be a problem, since the Sox seem willing to sign athletic players to long contracts (Crawford).