Bush still having a hard time connecting the dots between low taxes and LESS GOVERNMENT (”compassionate conservatism” (translation: “more government”) notwithstanding).
A truly compassionate conservative is interested in results — not throwing (other people's) money at perceived problems, because it feels good (like a liberal). If you were to eliminate the government programs that don't work (or are counterproductive); there would be plenty of money freed up to spend on programs that do help, while still reducing taxes.
Also, study the Laffer Curve. Lower taxes don't necessarily lead to less government — they may actually produce more government revenue. Some of that revenue could be used to reduce the debt.
Lower taxes promote economic growth. Lower government debt promotes economic growth. Economic growth produces more economic opportunities for people. More economic opportunities = fewer people relying on social welfare programs. That's something a compassionate conservative would hope to achieve — and it's something that sets him apart from a tax-and-spend liberal.