Article I, Section 8 of the Constitution grants Congress the authority to "To coin Money, regulate the Value thereof, and of foreign Coin." The chartering of national banks as a means of currency regulation might be interpreted as an exercise of this authority. However, in 1913, the Federal Reserve System was established and given the power to regulate the supply of money and credit, supplanting the old National bank system. Despite the elimination of the original justification for national banks, they remained in existence and new national banks have been chartered to this very day.
As for Federal deposit insurance, such as offered by the FDIC and the NCUA, there is no Constitutional justification for these agencies. Article I, Section 8 refers to the minting and valuation of coin. It says nothing about deposit insurance. Both the Comptroller of the Currency and the various State bank regulators require the obtainment of Federal deposit insurance, making its use and resultant supervision by the FDIC mandatory. There is simply no Constitutional warrant for the numerous business and consumer regulations imposed by the FDIC and other Federal banking authorities. The requirement for mandatory IDs to engage in banking transactions is yet another regulation unsupported by the Constitution.
As for the concept of a national ID, again there is no Constitutional justification therefor. The "interstate commerce" clause of the Constitution, also in Section I, Article 8, had as its original intent the prohibition of tariffs or other trade barriers to be imposed by the states. It was never meant to be a means by which the Feds can intrude on a myriad of areas, such as banking, medicine, food production, management/labor relations, etc.
Somehow this nation fought two world wars and major conflicts in Korea, Vietnam, and Kuwait without resorting to national ID cards or interfering with freedom of travel. (Of course, young men of military age were routinely questioned if not in uniform, but the rest of the population was not subject to the sort of restrictions that have already been or are proposed to be imposed.}
America is supposed to be a nation of laws, not men. We should respect the Constitution as the Framers intended under the doctrine of original intent and abandon the "living document" farce that has led to a massive expansion of governmental authority starting in earnest with the New Deal.