Let's look at some issues which are paramount in the USA.
Health CareI empathize with those who need health care for themselves and their loved ones. While there are of course tradeoffs involved (health care for more people == less money for other things) there is no question in my mind that the richest country in the world has an obligation to at least provide health care for every citizen.
TaxationI believe in progressive taxation because I have more sympathy for those in lower income brackets than those in higher ones. I believe Americans who have gotten wealthy in America (or have accepted the benefits of residency/citizenship) have an obligation to give back to those less fortunate, through taxes and through other means. I have less sympathy for millionaires who have to pay a higher percentage of their income simply because they have more than enough.
Gay MarriageI empathize with people who want to marry the one they love. I have no sympathy for those who wish to deprive other people of rights they themselves hold. I don't believe that there is a significant downside to gay marriage in the form of harm to children or society so for me it's an easy decision.
Religious FreedomI empathize with people who hold strong beliefs. I am therefore for total freedom OF and FROM religion for all. (However, your right to freedom ends when it curtails other people's freedom. Forbidding other people to marry because of your own religious beliefs is not acceptable but wearing a burqa, yarmulka, cross, or whatever should always be allowed.)
AbortionI sympathize with the teen girls, the rape victims, and the single women without sufficient income or health care more than I can sympathize with a fetus which has no self-awareness and can't even feel pain. Therefore I am strongly for legal early- and mid-term abortions. (Probably late-term ones, too, but that's touchy. I'm not totally convinced either way.)
Gun ControlI sympathize strongly with victims of gun violence. However, I also sympathize with those who need to defend themselves and I sympathize with the American people for whom the Second Amendment may ultimately provide the last defense against tyranny. I remain ambivalent.
Illegal ImmigrantsI sympathize strongly both with people trying to make a better life for themselves and for people who may be hurt by illegal immigration. My belief, however, is that, on the whole, more good than harm would be done by granting illegal immigrants work visas and a path to citizenship.
Flag BurningAlmost every election cycle, the Republicans bring out the Flag Burning Amendment. I have little sympathy for people offended by the burning of a flag (just as I have little sympathy for people offended by drawings of Mohammed) and I have a lot of sympathy for people in general, who require free speech, especially free political speech, in order to ensure the most just government possible. I therefore strongly oppose this ridiculous amendment.
Ten Commandments Monuments, etc.I have no sympathy for people who want to make it look like their religious beliefs are the beliefs of all Americans. I have a lot of sympathy for the people who history and current events alike show are much better off when church and state are separate.
For whatever reason, on the overwhelming majority of issues, the liberal position fits better with a morality based on empathy and sympathy for all. This is not to say that all conservatives are lacking in those traits -- there is certainly a subset of conservatives who honestly believe that conservative policies are better for all and that therefore being a conservative is the empathetic and sympathetic choice. However, I believe that most conservatives believe either that (1) what God wants, as they understand it, trumps sympathy or empathy, (2) that it's a dog-eat-dog world and economic freedom trumps helping the less fortunate, or (3) that some people are less deserving of empathy and sympathy than others.