In the event of a rejection by your construction employer to increase your pay after you ask, do you resign or continue to stay on and be embarrassed each time you see your construction employer? I love my job but yet underpaid.

If your request is rejected you really have two options: one is to quietly initiate a job search - keeping in mind that it's always easier to find a job when you have one - or get over being embarrassed and continue doing your job to the best of your ability.