No. They have the ability to make a uniform Rule for Naturalization, not to decide who does or does not fit the criteira of who is or is not a 'born citizen'.
Although Story was speaking of commerce, the idea is the same.
§ 1075 ................... But that is not the point in controversy. It is, whether congress has a right to regulate that, which is not committed to it, under a power, which is committed to it, simply because there is, or may be an intimate connexion between the powers. If this were admitted, the enumeration of the powers of congress would be wholly unnecessary and nugatory. Agriculture, colonies, capital, machinery, the wages of labour, the profits of stock, the rents of land, the punctual performance of contracts, and the diffusion of knowledge would all be within the scope of the power; for all of them bear an intimate relation to commerce. The result would be, that the powers of congress would embrace the widest extent of legislative functions, to the utter demolition of all constitutional boundaries between the state and national governments.
Joseph Story, Commentaries on the Constitution
I hear ya.
Our National Legislature indulged the foreign-born child with presumptive citizenship, subject to subsequent satisfaction of a reasonable residence requirement, rather than to deny him citizenship outright, as concededly it had the power to do, and relegate the child, if he desired American citizenship, to the more arduous requirements of the usual naturalization process.If, as SCOTUS suggests, statutory citizenship at birth is a Congressional generosity and such persons have no constitutional right to their citizenship, then their citizenship can be revoked without their consent by a mere act of Congress. The same is not true of 14th Amendment citizens.(...)
The proper emphasis is on what the statute permits him to gain from the possible starting point of noncitizenship, not on what he claims to lose from the possible starting point of full citizenship to which he has no constitutional right in the first place.
I really, really like Ted Cruz. It bothers me that his citizenship is dependent upon the whims of Congress. Political tides rise and fall. It was not long ago that Senator Lindsey Graham suggested that Congress revoke the citizenship rights of those born on U.S. soil to illegal aliens.