That is a general broad statement, hence the word "most". My counter is that you can replace "conservatives" with "liberals" and the statement would be equally as accurate.
Not really. As a generalization, conservatives favor the status quo while liberals favor change, that's why liberals are called progressives.
Just look at some major political positions. Liberals want to change the status of gay marriage, conservatives want to keep it the same. Liberals want to radically alter health care to a more universal system, conservatives want want small improvements to the existing private system. Liberals would banning guns, while conservatives want us to keep having them. Liberals want to get rid of the death penalty while conservatives want it to remain.
The in the few situations where the situation is reversed, it's usually around an issue that has recently been altered. For example, abortion is legal and liberals want it to remain so while conservatives want that to change. However legalized abortion is a recent development. Conservatives want to change it back
. The same for states where gay marriage is already legal. Conservatives favor change there, but they favor changing it back
to how it was before.
The very word conservative means to be predisposed to existing conditions and cautious of change.