Two distinguished scholars explore its original meaning. First, poitical scientist Edward Erler:
Most revealing, however, was Senator Howard's contention that "every person born within the limits of the United States, and subject to their jurisdiction, is by virtue of natural law and national law a citizen of the United States." Almost everyone certainly would have understood "natural law" to refer to the social compact basis of citizenship, the basis for citizenship adumbrated in the Declaration of Independence.
The argument of the Declaration grounded citizenship in consent. The natural law argument of the Declaration was a repudiation of the notion of birthright citizenship that had been the basis of British citizenship (i.e., being a British "subject") ever since it was first articulated in Calvin's Case in 1608.
Next, law professor John Eastman:
Such a claim of birthright citizenship traces its roots not to the republicanism of the American Founding, grounded as it was in the consent of the governed, but to the feudalism of medieval England, grounded in the notion that a subject owed perpetual allegiance and fealty to his sovereign.
So is "Born in the U.S.A." an anti-American song? No, as long as we agree through democratic republican principles. "All men are created equal" means that Americans are free to determine their destiny through proper means--not through the aristocratic principles that underlie birthright citizenship. In the current debate over illegal immigration, the true egalitarians here, the believers in the Declaration of Independence, are not the "birthers." This nation long ago stopped recognizing "squatter rights."
UPDATE: See at least this earlier post on the 14th amendment, with Richard Adams' comments.