No, don't give up but study funding possibilities, start with http://www.findaphd.com/students/funding.asp . You may also ask the department you plan to apply to.
I agree that 10,000$ would not be enough to finance a PhD, in my opinion it would only cover your living costs for 1 year (and you would have to be really careful about money and hardly buy anything), tuition fees excluded. As for the possibility of getting a job, consider two things:
-As an international student the number of hours you can work will be limited (I think 20 hours per week).
-Although many students manage to find a part-time job, maybe you will just have bad luck and won't find any. That can happen as well so don't rely on this possibility.
I think the better thing is to start a PhD having already a good idea on how you will fund it (already awarded scholarships, savings...) so that you will be able to finish it even if, during the 3 years, you don't get a part time job, extra funding...