Well, the Federalists weren't the only ones invited to the party, remember. The Antifederalists insisted on the BoR, and those Amendments seriously altered the nature of the compact, and of the federal union -- thus Elaine Scarry in the article I linked to, on the Second Amendment and the nature of consent and the distributed power to grant it in the U.S. Constitution.
The interposition of the inviolability of the Militia, of the jury-box, and of regular elections of the House directly by the People all guaranteed that the power to consent would not be a threshold exercise, used only once, but a perpetual or continuing exercise in consent. Likewise, the Tenth Amendment explicitly reserved all powers not granted in the Cosntitution to the People and the States (same thing) -- which, until Lincoln and, later on, the Commerce Clause prostitutes, seriously crimped the amount of practical power the federal Executive and Congress could take into their hands.
This was a huge change -- and it was the without which not that sealed the deal. Which the Federalists promptly tried to go back on, and eventually, with Lincoln, succeeded, using the instruments of war.
The Bill of Rights, I would say, amplified the original text of the Constitution, rather than changed the terms of the document. In fact, in convention, when George mason suggested a "Bill of Rights," every state voted against him.
The Federalists had argued that "too precise an enumeration of the people's rights was dangerous, 'because it would be implying, in the strongest manner, that every right not included in the exception might be impaired by the Government without usurpation.'" (I'm sure you see here the inspiration for the 9th Amendment.)
Gordon Wood wrote, "In a crucial sense the Antifederalists had lost the struggle over the Constitution when the New Jersey Plan, embodying the essential character of the Articles of Confederation, was rejected in the Philadelphia Convention in favor of a national republic stemming mostly from and acting on individuals. Faced with this national republic instead of a league of independent states, the Antifederalists were compelled to argue its merits on Federalists terms.... the question could no longer really be the one the Antiffederalists would have lied: should America have a national republic or a confederated system? but necessarily had to be the one the Philadelphia Convention had dictated: what should be the structure and powers of this proposed national government?"
It remained, then, for the Antifederalists to do their best to limit the powers of the "general" government. To this end, they agitated for a Bill of Rights. Once the Constitution was ratified, Madison was more than happy to change course in the 1st Congress and present a Bill of Rights on his own terms, rather than those of the Antifederalists. It was a political calculus and it worked. Madison was careful to propose nothing that substantially altered the intent of original text.