Can a construction employer withdraw an offer because you negotiated yourself out of the ballpark?

This rarely happens- but anything is possible. You don't want to come across too needy but if you feel that the position is worth it and that the employer can indeed come up with some more money. Go for it! People rarely get offers withdrawn due to what they are asking but how they ask.
Keep in mind these things: preparation, confidence and a willingness to walk away. To get what you want you need to have confidence that you bring value to the construction employer and if they do not recognize it they are not the right construction employer.