First of all, some people here is wrongly associating Ram to Hinduism. Whether Ram existed or not has nothing to do with Hinduism. Hinduism existed before Ram and still exists. It is a belief, it is a way of life, it has nothing to do with Ram.
This should not have been an issue at all. Whatever be the religious sentiments that should not create any problem for development project for the nation. All people, from all sectors will be benefited from the project. Then why the government have to listen to one section of the public? I am Hindu and I do not care whether Ram existed or not; why my opinion should not be counted? If the government really take a poll, it will be surprised to find that most of the people do not care about whether Ram existed or not.