There is a parallel phrase on the left: "socialism with a human face," as though regular socialism was inhuman. (It is, but that's another matter.) If anything, this slogan is even worse, because the change it suggests is, by implication, only on the surface; socialism will remain what it is, but it will put on a smile to attract more followers. And although the slogan was coined by a Czech leader, the mere awareness of it outside of Czechoslovakia makes it an implicit criticism to socialism everywhere.
What if one wanted to emphasize the compassionate aspects of conservatism, but wanted to avoid the phrase "compassionate conservatism"? I don't have a catchy slogan, but it would have to emphasize the compassionate face of conservatism (implying that, although it has sides that are less compassionate, at least one aspect of it is already compassionate). I would also want to explain why I was choosing to emphasize compassion over other aspects of conservatism. After all, why shouldn't it be compassionate all the time? The reason must be that there is an appropriate time for compassion -- for example, after conservatism's hard-edged virtues had won the Cold War. So I would loudly announce that (for example), having won the Cold War, it was time for the nation to turn to the other side of the winning doctrine: the compassionate side. Not that I think there is a meaningful distinction between compassionate and non-compassionate conservatism; I'm just offering this as a proposition.
Obama's slogan, "Yes, We Can" is brilliant. It is positive and immediately throws anyone opposed to his programs on the defensive -- not only as obstructionists, but as people who doubt the capability of America to achieve great things. The opposition immediately becomes those who believe "No, We Can't," unless they can counter with an equally clever slogan that avoids creating a negative impression. (I don't have any ideas.) This slogan also happens to be the one used by Bob the Builder ("Can we build it? Yes, we can!"). I am shocked that no one, including conservatives, has noticed this connection. It ought at least to be good for mocking in editorial cartoons. I can't help thinking that if it were a Republican's slogan, we would be hearing about how he is setting himself up as a cartoon figure.