Joanna Lane has given you lovely advice about offering a little less, which is what I was about to say until I read her comment. The down payment assistance programs are slated to expire on Oct 1, so you also have time to try and receive funding from them. If you are funded and close before Oct 1 it may also be a solution. Google Ameridream and Nehemiah and see if you can get a down payment grant before the deadline. Wishing you well with your purchase.
1. Offer $4,000 less for the condo, and let them know it's a firm offer. All asking prices are negotiable. They can only say no, but equally, they may accept it, or counter offer $2,000, then at least you have halved your problem.
2. you can ask for an extended closing date, although I would hardly call 2 months extended. By that point you would have what you need, especially if you can get them to drop the price a little at the same time.
3. If none of the above works, talk it through with parents. It's only a temporary loan to help bridge the gap for a few weeks.
In the overall scheme of things, there's not much standing in your way - don't let it stop you achieving your goals. Go for it!
So any lower "firm" offer should probably be 5k less, because 80% of 5k is 4000.
You don't mention your job, any 401ks, any IRAs or any other assets, so I haven'tt commented on them.
Secondly, there is a program call the HomeFirst Down Payment Assistance Program. It sounds like you probably will be over the income levels, however I figured I would mention it anyways.