I think we do indeed need our rights as American citizens, perhaps not to survive; but life is certainly more than abject survival. If one considers the experiences of other countries where one never knew in the morning if he would be home that night or arrested by the secret police; where one's person, papers, effects could be searched at will; where one can be imprisoned without charge for years on end; where one might be tortured to secure a confession whether or not that confession is legitimate; then one must agree that the rights guaranteed under our Constitution are absolutely necessary to preserve the quality of life we have come to expect. If we reduce the meaning of "need" to nothing more than survival, then we have relegated ourselves to the "state of nature" which Thomas Hobbes described as "nasty, brutish and short." To say that we can "easily live without them" as the above answer states suggests a cynical existence which none of use would find bearable--billions of Chinese to the contrary notwithstanding.
The answer to this depends on what we mean by "need."
In a literal sense, we do not need these rights. We can easily live without them. There are, for example, over a billion people in China who survive well enough even though they lack the sorts of rights (things like freedom of speech) that we have.
In another sense, though, we do need these rights in order to have the sort of life that we all expect. I would not, for example, like it if the police were free to look through my home any time they wished. I would not like to be prevented from speaking out against the government if I so desired.
Most of us do not need our rights to survive, but we do need them to live the sort of life we feel we have the right to live.