Can I give up my house under chapter 13 if I just cannot afford it?

If all you want to protect is your cars, I wonder why you aren't looking at Chapter 7 as a better alternative? You can surrender your home and a receive a discharge of the mortgage liability under either Chapter. If you have a second mortgage on your home which is causing the property to be upside down, I would also look at a Chapter 13 scenario where you strip the lien held by the 2nd mortgage as often this will put you back in a situation where you are comfortable and able to keep your home.