Here is what I calculated. If you paid full MSRP, taking into account the 595 acquisition fee, a 7% sales tax (I believe this is what NJ has), with $2,500 down and no other fees you would be at about $265/month. That is assuming a 12,000 mile lease with 59% residual and .00087 money factor (This was the lease info when I got mine and I believe they still hold true). In any case your quote is just INSANE! (unless you meant you were getting an SE with Nav and sunroof and not without) Then it would be a little more reasonable. It looks like the selling price would be about 26,500 to put you in the $350/month payment range.
Now personally I would say, you shouldn't even be paying full MSRP. I'm a business minded person, so I understand the dealer needs to make a profit. That being said, picking it up for 500 or 1,000 under MSRP and the dealer will still make a nice profit and you will get a pretty decent deal. Even if you don't feel like haggling, it should be prettty easy to get a dealer to that range. Just make sure they don't charge you like $500 for document fees. A $100 or so fee would be reasonable for this and again just adds to their bottom line.