"Wording aside, should foreginers born here be immigrants?"
It's not a wording issue.
A person born here is not a foreigner. He's an American, and therefore not an immigrant.
What you probably mean is: should the child of foreign parents born in the US be an American? The Constitution says they are, so they are. SHOULD they be? I think so. It's the only way to eventually regularize the illegals in America. As it is, there are about 20 million illegal aliens in America. The economic interests that use them are stronger than the old slavery interests ever were, because the slavers were concentrated in one part of the Union, but the economic interests who benefit from cheap illegal labor are all over the country. The inaction of the federal government and state and local governments on the illegals issue is the natural response of government faced with the truth that the middle class and up all rely on these 20 million unprotected workers for cheap labor that is below the norms of US labor law.
Now, so long as their children are Americans, because born here, this subjection of one illegal class of workers to the society is non-permanent. They come and work. The society at all levels, from middle class people with yard-work to do to WalMart, breaks its own laws because it's economically good for them to do so. The immigrants themselves are not protected, and can't be protected because the advantages of exploiting them are too strong, and the financial incentives, from there perspective, to come and stay here are too great.
What you cannot do is let them become a hereditary race of unprotected, illegal laborers. That would be a gross injustice. Americans have a hunger for this cheap labor, unprotected by American laws and without recourse to the American courts. That is understandable. If they want that sort of labor, they have to keep importing it. They cannot be allowed to make it an hereditary caste.
Babies born in America are Americans, and move into the system of protection. Close the borders, and in a generation the cheap illegal labor pool will dry up.
Their children will be Americans, and protected, and vote. That is as it should be. It is what's best for the country, in the long run.
If the borders won't be closed, you'll always have the cheap labor, but it will keep having to be removed, because there will not be a class of legal "sudras" in America, born of illegals and, therefore, hereditarily unprotected.
"Regularize" the illegals?? McCain is that you?
We don't need to regularize anybody whose first act in our country was to break the law. Enough is enough of doing that, it's already been done several times and been proven a failure, it only encourages more of the same.
If it werwn't for welfare, a lot (but not all) of the problems of illegal immigration would fall in one fell swoop. They wouldn't be such a burden on taxpayers and the system when there is no system. Not to mention that welfare is bad for Americans.