If you decide to stay, how you handle this situation and how you get to the end of the project will be remembered by everyone involved. Assuming you dig in, do the best you can and try to keep your chin up, this can help lead you to better opportunities on new projects where you are asked for by name. Also, the relationships you make now, can also follow you and can be leveraged down the road as the company grows and as you maneuver through the growth of your career.