The role of government in ensuring rights: Government (the people who govern) exists off of taxes. In order to get those taxes, government provides protection to the taxpayers so that they can have a stable enough society to produce taxable wealth. People want protection so that they can pursue happiness. Happiness is adequate food, clothing and shelter for self and family, and knowing that no one is likely to come along and take it away from you. People pay taxes to government in order to get protection from government. As long as the taxes are not too high, or the protection too little, a stable, happy society exists.
Government should protect everyone in his freedom to do whatever does not hurt anyone else.
There is no right beyond protection that government can provide to one individual or group without first taking it from another individual or group. So I would answer the second part of the question by saying, there definitely can be too many rights.