"Compassionate Conservative" should be a redundancy.

Nothing about conservatism implies a lack of compassion. That the media portray conservatives as lacking compassion shows just how far we've skewed ourselves from a true, and important, meaning.

George W. Bush first used the phrase in public in 1999 to introduce himself to Republican voters.  For him (as for many things about him) it was a political compromise, to appeal to conservatives in the Republican party, but not to jettison moderates from paying attention.

Once Bush had clout , he should have clarified, as I will do for him here:
conservatism IS compassionate.

Conservatism abhors bilingual education because conservatives know that letting a Latino American student feel good while keeping him from being immersed in English cripples his chances at a good career.

Conservatism doesn't extend unemployment insurance benefits automatically, because the most compassionate thing for an able job seeker to compel him to get himself back into the work force right away.

"Free money" is a teat that everyone wants to milk.   If offered for a long time, it's a difficult addiction to break free of.
Conservatism dislikes illegal immigration because of our compassion for the immigrants and would-be immigrants who have gone through long, arduous legal channels to emigrate here correctly.
Our compassion extends to American-born citizens, particularly African Americans, who see their jobs jeopardized by illegal immigration.

The fans of illegal immigration are less compassionate to marginal Americans than anyone. Conservatism likes the death penalty for murderers, because it is the most compassionate thing for victims' families (and it's just, and the Bible warrants it, and it just may deter future murders).

So I ask Republicans (this is a Democrat speaking to you): stop liquefying a rock-solid word "conservative".

Donald Trump did a disservice to this word too."I'm conservative, but I have a big heart", he said to Megyn Kelly in May 2015.
Again, conservative should imply big-heart; now show the public how.

Compassionate Conservative