As someone stated, when writing your offer, you can ask for closing cost assistance from the seller if cash out of pocket is a key factor for you. You may end up paying a little more in the asking price, but it would save you the out of pocket expense.
Another thing that lenders can do is "credit you" if you take a slightly higher interest rate. I had a client that we ended up having to do this in order to make the deal go through because the seller didn't have any extra funds to help with closing cost assistance even though they had agreed to it originally. She was able to get a credit for $1,800 from the lender and her monthly payment went up by about $12. To her it was worth it because she really wanted that home and didn't want to have to look for another, but she didn't have enough money to cover the closing costs herself.
Depends on how you approach it, but $2k doesn't seem to bad.