Of course, the Constitution doesn't grant rights. Do you have a natural right to be left alone if you so choose? Do you have a natural right to not be a witness against yourself? It seems a society based on popular sovereignty should define these rights as inherent and innate to being a person.
And if you do assert your Constitutional rights, it's an easy way to escalate a situation where you soon learn the meaning to "you can beat the rap, but you can't beat the ride."