Conservative means what it has always meant. The political belief that the law should bind outsiders but not protect them and that it should protect insiders but not bind them.
In most cases, you'd probably be correct in thinking that the person would be more inclined to preserve the status quo than changing it too quickly, for fear of unforeseen consequences.
Also, a simple Google search and 30-second skim of Wikipedia throws a wrench in your assertion.
This does not encompass reactionary conservatives that have become incredibly prominent as a political group in the United States, to the point of completely taking over one of the two political parties.