Yeah not gonna lie, this would be a shiet trade for us IMO. First, for those first 3 players, Cano alone should be able to bring them in. You are talking about one of the best hitters in the game and arguably the best second baseman in the game.
Brett Gardner, although he missed almost all of 2012, was the 2nd best left fielder defensively in 2011, and is also arguably the fastest man in baseball. And the guy can work a count as good as anyone. If he can get on base often, he can be a dynamic player. But that remains to be seen.
Eduardo Nunez, as of now, figures to succeed Jeter at SS. Nobody doubts his hitting ability, he just needs to iron out his defense.
Betances is one of our top prospects, but he did go down with an injury, is still unproven, and got demoted to Double-A.
Grandy looks like he's staying, and if we lose him, who do we replace him with? Especially since we are trying to get under 189 million by 2014 so we can't exactly make a big splash. So not only are you losing Grandy, you're losing his possible replacement in Gardner.
In my opinion, this trade would not work out, and would actually make us slightly worse. Headley is overrated, and we can't put him at 3rd because of A-Rod. We have Jeter at short, so where does Elvis Andrus fit in? And we still need to find a way to replace 2 of our starting outfielders, so with Swisher walking as well, we have no outfield. Doesn't work in our favor.