The Founding Fathers intended for and expected the Constitution to be openly and honestly amended or replaced much more than it has been. The Madison quote is actually warning that if we do not update the next of our Constitution and laws to match changes in our language that their meanings will change so as to allow things that the public never meant to authorize, essentially saying that the constitution needs to be updated so as not to become a "living document." They were very much opposed to what "living document" is taken to mean today, where the sophistry of the judges (particularly but not only the justices of the supreme court) is allowed to fundamentally change the meaning of the text to something that disagrees with the intention of those who gave the document its authority by voting to ratify it.
The "living document" notion was invented by President Woodrow Wilson. It was meant to be a more palatable replacement for the view he espoused earlier in life, which was that the Constitution was just a worthless piece of paper that should not be allowed to prevent the government from doing absolutely anything that it wants to do. Wilson is often considered one of the "Progressive" presidents, but his views were pretty much Fascist. His admirers included both Mussolini and Hitler.
Thomas Jefferson was among the foremost advocates of interpreting the Constitution very strictly. (He was a little hypocritical while in office though, in that he agreed to the Louisiana Purchase without first requiring a constitutional amendment to allow such an agreement, as he had claimed would be required.) He was also of the opinion that we as a nation needed to have a new revolution every generation. He did not mean a violent overthrow of the government as some have claimed. Rather, he meant that we as a nation should start fresh and create a new constitution every few decades, in order to give each generation a chance to ratify the government under which they were to live. Since the government derives its power from the consent of the governed, he did not consider it right for a constitution to be binding on a generation that was never given a chance to consent to it. Also, while he was very much in favor of decentralized power in his day, he expressed the belief that population growth would make a somewhat stronger and more centralized state necessary starting sometime in the 20th century.
At the time of their ratification, the Constitution and the Bill of Rights were considered binding on the Federal Government, but not on the State governments except where that is explicitly stated. The first amendment begins "Congress shall make no law..." and was very clearly considered to only apply to the United States Congress. The several states were still free to make laws respecting religion, speech, etc. Likewise, the second amendment was seen as prohibiting the Federal government as intervening in the affairs of the state. A "well regulated militia" was the defense force that each state could use to defend itself not only from invasion by foreign powers but also from the federal government when it overstepped its bounds. The Feds could not prohibit states or localities from making, importing, or using weapons to defend themselves. The idea that the second amendment would be used to strike down local ordinances pertaining to gun ownership would seem absurd to the Founders. Many of the oldest cities in America had firearm regulations dating back almost to their founding, and most states had laws prohibiting slaves from baring arms. Some states borrowed that British law that required landowners to own firearms and forbid them to anyone else.
The biggest issue when it comes to the interpretation of the Constitution is whether the Bill of Rights is Incorporated against the States by the 14th Amendment. These days the court tends to view it as incorporating the whole bill of rights, although when it was ratified it was generally believed that it simply ensured that the Civil Rights Act of 1866 could not be ruled unconstitutional. There is also considerable controversy as to whether the 14th amendment was ever legally ratified. Many Southern States were essentially forced to ratify it by the Union Army that was still occupying them. One state was only able to get a quorum large enough to ratify it by kidnapping several of the opposing legislators and holding them prisoner in the legislative chamber against their will. A couple states voted to reject it after ratifying it (in one case because a ballot recount found that many of the legislators who voted the first time had not been duly elected), but the Federal government still counted them as supporting it.
None of the Founding Fathers had anything to do with the party that would become the modern day Republicans.
The first (informal) parties were the Federalists and the Anti-Federalists. The Federalists (including George Washington, Alexander Hamilton, John Adams, John Jay, and James Madison) supported the US Constitution. They tended to be businessmen who favored having a more powerful central government and mercantilist trade policies. (Remember that the current Constitution was a huge Federal power grab when compared to its predecessor, the Articles of Confederation.) The Anti-Federalists (including Thomas Jefferson Samuel Adams, James Monroe, and Patrick Henry) were a much larger group that opposed them. They tended to be more agrarian and more classically liberal. They were very much concerned that the Constitution did not do enough to protect individual rights. They are the group responsible for the Bill of Rights. They only compromised and accepted the Constitution when it was promised that the first act of Congress would be to pass the Bill of Rights for the states to ratify. Since they did not want the government to be as strong a the Constitution allowed, they were vigilant to prevent it from becoming any stronger than the document legally allowed.
(Hamilton was not only a mercantilist but also a monarchist, who wanted to make George Washington a king and hoped to be his heir as he had no children of his own. I get really upset when I hear people use John Adam's support for state supported healthcare for mariners as proof that the recent healthcare bill is constitutional, considering that "His Rotundity" Adams also strongly supported the Alien and Sedition Acts. This made it a federal offense to criticize the president, and sent people to jail for exercising what is clearly protected free speech.)
After the Constitution and the Bill of Rights were ratified (note that some states only ratified after a largely Federalist Congress threatened them with trade sanctions), an Anti-Administration party was formed by many former Anti-Federalists and a former Federalists like James Madison who opposed the policies of Treasury Secretary Alexander Hamilton. This group evolved into the Republican Party when Thomas Jefferson became their de facto leader. This is not our Republican Party however. This Republican Party soon became known as the Democratic-Republican Party, and then eventually evolved into the Democratic Party of today. After the Jefferson became president, the Federalists lost most of their power and began to die off. (They continued to control the courts for a while though, as they used a lame duck session after loosing reelection but before leaving office to greatly increase the side of the judicial branch and pack it with Federalist judges appointed for life.) The Democratic-Republicans were the only major party (although it was a big tent party containing many factions) until the Whig Party organized in opposition to the policies of Andrew Jackson. The Whigs supported the supremacy of Congress over the growing power of the Presidency ("King Andrew I" was somewhat dictatorial and corrupt, although not so much compared to modern presidents), and like the Federalists favored Mercantilist, Protectionist policies over economic liberalism. Whig presidents tended to be war heroes without any real political philosophy. The party eventually collapsed.
The first president from the modern Republican Party was Abraham Lincoln. The Republican Party formed shortly before the Civil War as a union between the Free Soilers (those who opposed the spread of slavery into the territories, although most were not principled enough to actually advocate the abolition of slavery where it already existed and some even opposed the spread of slavery on the grounds that they did not want any blacks living near them) and the remnants of the Whigs. They were very much a pro-business party from the start. At the time, this meant favoring Protectionism and large Subsidies to Corporations such as the railroads. It took decades before they began to pretend to favor free market instead of simply supporting the wealthy capitalists who in turn supported them with campaign donations. Probably the first actually principled Republican president was Calvin Coolidge.
