The US Constitution doesn't grant rights to people. The people have these "inalienable rights" as "God given". Rather it limits the power of government. For example, the 1st Amendment says: " Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances."
Or in the gun case: 2nd Amendment: "A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed."
In both Amendments, you see that it is the government that is limited. Nothing is granted to the people. They have these rights to begin with. That's a powerful message. It reminds government officials that they don't give anything to people. They take things away, only if the constitution allows them that power.
The Constitution enumerates powers that the federal government (national in DC) has. Such things as maintaining an Army, making treaties, regulating interstate commerce. It then says that those remaining powers not granted to the national government are left to the individual sovereign States, now 50, and then to the people themselves. So the individual states which are also sovereign can have their own Constitutions and issue laws for state taxes, highway speed limits, state taxes, etc. As long as the state law doesn't conflict with rights in the Consitution, the State follows the majority rules through their own legislatures. All remaining power is left with the individual to do whatever they want to do.
As Phil posted above, you don't want a Congress or legislature to change these laws by popular vote because then these rights can be washed away during a crisis or under emotional appeal of the majority. The restriction and rights are there to protect the minority. Majorities don't need protection because they have the vote to change the law. That's why Nazi's can speak their mind even if 99.9% of the country disagree with what they have to say. Or in the Las Vegas situation, if let's say 75% of the people in the country want to ban guns, the 2nd Amendment prevents Congress or the individual States from doing that. The emotions of Las Vegas will not allow gun owners, a minority, to lose their arms. An Amendment to the Constitution is required.
I think the Constitution has been interpreted or mis-interpreted taking rights away from people in certain areas while limiting government more in other areas. On balance, the Constitution seems to be working for us. Our government hasn't been over thrown and we're still running strong after 230 years.