Well, "conservative compassion" tends to involve economic conditions whereby millions starve to death in the streets, while a very few get extremely rich, and give a few bucks of their billions, now and then, to pay for opera houses, and once a year a meal for a couple of people, OR a meal a day, only if the hungry will accept the rich people's religion to be forced on them.
In other words, conservative compassion has hardly any compassion to it at all. Mostly, it involves allowing the few to keep almost all of the profit of everyone else's labor, while most struggle or starve.
We live in a representative democracy. The Constitution says that one purpose of government is to "promote the general welfare" (make things better for citizens in general).
Since most Americans have the REAL kind of compassion, where we don't want the maximum needless suffering, but minimum, those who represent us allocate our tax money toward that general direction.
Yes, the desire of conservatives to create an economy where 1% of the population owns 90% of the wealth, and everyone else are their slaves IS among the issues causing the most friction between conservatives and everyone else.
It's simply not true that liberals have the power to control where tax money goes, most of the time, without support of the majority of Americans (and even with that support, the Republican party tends to force its unpopular agenda on the nation a lot of the time).