There's a specific method for amending it that requires a very high level of agreement among both houses of Congress and the various state legislatures. In theory Congress or the executive branch could just ignore that and go do whatever they want as long as the judiciary didn't stop them, or the Supreme Court could use weasel-words to make the Constitution mean something other than what it says. Both of those things have happened to varying degrees over the years, but it would be a huge expression of contempt for the rule of law for anyone say outright that was what they were doing.
Australia has constitutional referendum as well, these require a 'double majority' (from the public) to pass as well as an absolute majority in both House of Parliament. Which means it needs a national majority of voters AND a majority of voters in a majority of states and territories.
