Anchor babies and US Citizenship

I heard Mark Levin talking about this subject (automatic citizenship for the children of illegal aliens born in the United States) and why the current interpretation of the 14tha amendment is wrong.  I'm going to try my best to let you know what he said but I'm sure I won't do it justice.

First of all, here is the relevant part of the amendment:

14th Amendment

Section 1.

(Bold is mine)

All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside. 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.

Mark's main points were as follows:

If this amendment meant for ALL people born in the US to have automatic citizenship then why did they include the phrase "subject to the the jurisdiction thereof?"  They could have left that out ... but they didn't.

Q - If a tourist, who is here LEGALLY, has a baby here, is it automatically deemed to be a citizen?

A - No

Q - If a LEGAL diplomat has a child born here, is it automatically deemed to be a citizen?

A - No

Why is this?  It is because of the phrase "subject to the jurisdiction ..."

-- END OF MARK'S POINTS --

My extension of the above:

Then why, pray tell, are the children born of people who are here ILLEGALLY considered citizens?

Does this make the SLIGHTEST bit of sense to you?  Do you detect an incongruity here?  Does this make your sense of right and wrong tingle a bit?