The Founding Fathers did not want no government, they wanted limited government, and they correctly recognized that government is the greatest threat to our liberty, so they bent over backwards to limit it. So, heres how todays major parties and ideologies view it.
Pro Constitution
Small L libertarians We love it. They wrote it right, they recognized the real threat is government. We just want what they created. Generally our differences with the Constitution is we wish they hadnt said things like the General Welfare, which is just opening the door to those who dont care what it means, even though it doesnt mean what they want.
Small L libertarians want a small, fiscally conservative government, the military to be used strictly for the defense of the United States and dont want morality laws. Exactly what the founding fathers wrote.
Small government conservatives Small government conservatives mostly overlap with libertarians. The biggest differences are generally military where they are more willing to use the military overseas than libertarians and they are generally more open to policies like fighting drugs. At some point they will hopefully realize the problem isnt what they want, but that government is the problem and not solution to those objectives as well.
Anti Constitution
Social Conservatives Social Conservatives are generally fiscally conservative, but fiscal conservatism just isnt their priority. While they talk about small government and our making our own decisions, they just ignore that there is no Constitutional Authority for morality laws and that government making morality laws isnt small government.
Neocons Pretty self explanatory, they are for high military use and big government spending. They are generally less interested in morality laws, but even that just isnt the priority.
Big L Libertarians (the party) They dont like the Constitution because the two parties fight over it, so they associate it with the two parties. Theyre elitist snobs and consider themselves above it regardless of what it says.
Anarchists They dont like the Constitution because the founding fathers wanted limited government, not no government. Anarchists are simple minded and naïve and dont really have any solutions to anything, so they fight all solutions, even the minimal solution.
Liberals Liberals are intellectual scavengers. They like the Constitution in a sense, but they dont really know or care what it says. Since it is the law of the land (or was), they just quote it if it seems to serve their purpose, parse words if it doesnt, get the courts to make law if they can and just say that times have changed to justify what they want and say the Founding Fathers would be liberal if they were alive today anyway.