But what should she have said?
Let's set aside the question of God for a minute. Let's interpret "god-given rights" to be human rights, those rights that all individuals deserve, simply on the basis that they are human beings. The Declaration of Independence (and NOT the Constitution, as Sen. Grassley claims) discusses these rights.
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their creator with certain unalienable rights, that among these are life, liberty, and the pursuit of happiness...
It goes on to say that when a government aims to usurp these rights, the people have the right to reject that government and build a new one. And that's just what they did.
The Constitution outlines the new government in some detail, including the roles and powers (including limits on those powers) of each of the three branches of government and how members of those branches are elected or chosen. At the end, they set forth the rules for amending the constitution (how many members of congress or how many states must agree on the amendment).
The amendments (including the first ten, known as the Bill of Rights) add more detail on the powers of the government. Sen. Grassley quoted the second amendment (commonly known as the right to bear arms), and asked Kagan whether she believed that was a god-given right or a government-given right, and then explained (using different words) that the government giveth, the government taketh-away.
Now, I'm certainly no expert in Constitutional law, but I do have a copy of the Constitution. With a cursory examination, I don't see any delineation about whether the rights afforded in the Constitution and its amendments are among those unalienable rights described in the Declaration of Independence, or they're additional rights granted by the government. I suppose that's why interpretation is so important.
Perhaps the most important and all-encompassing amendment is the 14th, which starts off with a blanket statement:
No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
So it sounds like citizens get privileges and immunities, but all people within the US jurisdiction (citizen or not) get life, liberty, and property (unless they are lawfully convicted of a crime), and all people inside the US also get equal protection of the laws.
Equal protection of the laws... I think that refers to laws like the 13th amendment (which abolished slavery in the US), saying that even if you're not a US citizen, you can't be forced into servitude/slavery. But of course it applies to all other laws and protections, too.
Some amendments are specific about whether they apply to citizens or all people, but the 2nd is not one of them. It states:
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.
Parsing the convoluted sentence structure, it says the government (including state and local governments) can't prohibit the ownership and carrying of weapons, and that's because a well-regulated and armed militia is necessary to maintain security.
It should be noted that none of the amendments in the Bill of Rights uses the term "citizen", but instead "the people".
So what should Kagan have said? Based on MY interpretation of these documents, I would say that the Bill of Rights was intended to protect the rights of US citizens, and the 14th amendment extends that protection to non-citizens within the US jurisdiction. I think if the government tried to revoke any of the rights described in any amendment, that would be justification to overthrow the government. (And in such a situation, it would be good to have a well-regulated militia.) So yes, the second amendment, like all the rest, is a god-given right that the government must recognize and protect.*
*Luckily, there's this loophole about a well-regulated militia and the security of a free state. Does it apply to private citizens or only law enforcement? Does it apply to private citizens in places where a police force is sufficient to maintain security? Does it prescribe regulations such as enforcing that anyone who bears a weapon be trained and/or licensed to use it?
Edited to Add: Interesting related story!
Finland has made high-speed internet access a legal right:
The government of Finland has also promised to make good on its goal of getting every citizen with a 100Mbps connection by 2015, saying that they now consider internet access a basic requirement of daily life.
Does this imply that Finland's government has recognized a god-given right, or granted a government-given right? Can a right be god-given if it didn't apply to people of the past? Was there a right to bear arms before arms were invented? Are these god-given rights really broader than that, as in the right to security, or the right to information?