That quote is an exercise in how logic can fail when it is based on fallacious assumptions. There are many avenues for discussion on this topic, but the part that catches my interest is the initially appealing sentiment of compromise.
When dealing with multi-issue, partisan platform politics, there is more than one kind of compromise to be had.
There are some topics on which both parties should learn to compromise... typically things of a technical nature like tax and economic policies, and other issues where ethical considerations and reason can exist on both sides, and where measured, careful change is healthy for the system as a whole.
There are some ethical issues where the impetus to alleviate immediate human suffering is strong, and the compromise should be more in the 2/3 variety. These are places where progress is necessary but fervor must be checked lest it run wild.
Then there are cases like abortion, where one party is the clear aggressor, and is typically motivated by irrational fear. The correct compromise in these cases is that the aggressor must simply give up on that issue. This is a give and take, however, and both of our major parties have issues that they should be prepared to drop if they ever want the support of the center.
This idea that giving in to the fringes to appease them would somehow move the parties to the center is, however, sadly misguided. History has consistently shown that the strategy of appeasement can only fan the flames of hatred.
The particularly egregious assumption in play here is the idea that savagely curtailing the rights of some is of equal value to appeasing the fears of others. Fear has no inherent moral quality, but freedom of choice does.