In a perfect world, many would have wanted the Jets to land Jay Cutler. Before there is any rush to anger over being beaten to the punch by Chicago, one must consider what the team would have been forced to give up.
The Bears surrendered two first round picks and a third rounder. They topped the deal off with a new starting quarterback, Kyle Orton. The Jets could have matched the picks, but they had no proven quarterback to swap. Gang Green would have needed to find an appropriate substitute for Orton. A few have argued David Harris would have fit the bill since the Broncos are switching to the 3-4 and have few quality defensive players. Orton is a mediocre starter, while Harris is a star in the making at linebacker.
While that explanation appears apt on the surface, the only point of view that matters is that of the Broncos. Few hold Orton in particularly high regard, but the decision-makers in Denver apparently are in that number. If the Broncos did not think they could develop Orton into a high quality starter, they would not have asked for his inclusion in the trade. They would have asked for someone else. The choice between Orton and Harris would be a choice between filling a hole at linebacker and filling one at quarterback. They probably would figure that linebackers are easier to find. The Jets probably would have had to sweeten the pot, maybe by throwing in a young star with a reasonable contract like Darrelle Revis or Leon Washington. In the process, they would have given away multiple cornerstone players and the chance to select others in the Draft.
One might argue the Jets could have kept Harris if they could have found a third team with an extra quarterback as a trading partner like the Browns. The team still would have parted with the two first rounders and a third rounder. Denver would demand that to match Chicago's offer. Those picks would have had to come from the Jets. Cleveland would not have given up its own picks just to trade a quarterback. In addition, the Jets would have been forced to give Cleveland a generous return. Quarterbackers are a rare commodity in the league. The Browns would need a lot of persuasion both to give up one of their proven signal callers and not persue themselves the upgrade Cutler would be for them.
Either way, Gang Green would have had to give up an astronomical amount to top Chicago's offer. This to bring a hyper-sensitive quarterback to New York. Cutler is not Peyton Manning. He has not turned teams into contenders by himself. If Mike Tannenbaum wanted to dismantle his team for a player, it would need to be for somebody in that mold, not Jay Cutler.