When American politicians claim a "fundamental difference" to distinguish themselves from their opponents, or when they say "we fundamentally disagree", they're using one of the cheapest and least-accurate idioms in the English language.
The "fundamentals" in America are simple: Life, liberty, and the pursuit of happiness. We all believe fundamentally in individual liberties, market economics, and the protection of the rights of the minority -- even when that's not popular with the majority. If you fundamentally disagree on those principles, then you're not really an American in spirit.
Where we differ is in matters of execution. We differ with one another in our own time, and we often have differed with our predecessors. Those individual liberties are better-protected today than they were 50 or 100 or 200 years ago; we've gotten better about that over time, and we'll continue getting better in the future.
We've changed course on exactly how to implement market economics many times -- Hamilton and Jefferson differed about whether the government should be able to carry a national debt. Andrew Jackson shut down the Second Bank of the United States. Teddy Roosevelt busted the trusts and brought about antitrust laws. Franklin Roosevelt fought with the Supreme Court over important matters of government intervention in the economy. Many of these occasions (and countless others) may have been transformative -- but they were never fundamentally deviations from a market economy. Major changes in course? Maybe. But never a fundamental sea change into Communism or feudalism or mercantilism.
If we're honest with ourselves, no matter how much people complain about "activist judges" or "overreaching courts", we all agree as Americans that we want some power to prevent the tyranny of the majority from trampling the rights of the minority, since we all perhaps realize that we are, on occasion, in the minority ourselves.
These things are fundamental. They are essential to the American way. If you want fundamentals, look at the Oath of Naturalization. Look at the Constitution. Look at the Declaration of Independence. These things are fundamental expressions of Americanism. Other things are details, and details upon which reasonable people can disagree without being fundamentally at odds with one another.
Hyperbole undermines the kind of healthy, rational arguments we should have with one another in a free society. We have differed fundamentally with Al Qaeda, with the Soviet Union, and with Nazi Germany. Calling our domestic opponents fundamentally wrong undermines the possibility that their minds might be changed -- or ours. And if we reject that kind of freedom to adapt and grow, then we're doing ourselves wrong.
"I am not an advocate for frequent changes in laws and constitutions, but laws and institutions must go hand in hand with the progress of the human mind. As that becomes more developed, more enlightened, as new discoveries are made, new truths discovered and manners and opinions change, with the change of circumstances, institutions must advance also to keep pace with the times. We might as well require a man to wear still the coat which fitted him when a boy as civilized society to remain ever under the regimen of their barbarous ancestors." - Thomas Jefferson