"Seventy-two per cent of Republicans think that the Constitution is basically fine as is; seventy-two per cent of Democrats disagree." Of course this has nothing to do the actual Constitution. It's a statement about each party's (dis)satisfaction with the current success of their party. The optimist in me wants to believe that even in this polarized culture politicians could compromise and find a middle ground on man…
Conservative values generally mean trying to keep things the same. A hard to change set of rules supports this. Progressive values generally mean trying to make changes [to improve society]. Being able to change rules supports this.
We should therefore expect conservative people to want a hard to amend constitution and progressive people to want a easy to amend constitution, regardless of whether or not they are in power. I expect this asymmetry to be visible in whether more ammendments are proposed (and ratified under) progressive or conservative regiemes.