I have always been able to understand the differences between the two groups by remembering the following.
Liberals core belief is that the average American is not capable of making good decisions and all of the important decisions should be made for them. If they do make a bad decision, they should not be held accountable for their bad decisions.
Example: if people do not have guns they cannot do evil things with them. If they do manage to do an evil act with a gun, we need to treat them with compassion.
Conservatives core belief is that all Americans should have the liberty to make all decisions that directly affects them. If they make a bad decision, they should be held accountable for that decision as a learning experience.
Example: if gun ownership is universal, people with evil intent will not have an advantage. If they do manage to do an evil act with a gun, they have decided they are not entitled to compassion.
It is not mistake that liberals occupy Venus, it is closer to the sun and runs hotter. Life on Venus is associated with higher activity levels. Mars is colder then the earth and life on Mars moves slower and more deliberate.
Liberals are driven by a desire to implement a theoretical belief while conservatives want to develop a model that proves the theory before it is implemented to minimize unintended consequences. This is why we are witnessing the debate over gun control in spite of examples that says gun control does not reduce gun crimes.
Given the above, it is not hard to understand that there is no common ground for compromise between the two groups. The only compromise between the two groups is one that minimizes the negative impact on their mutual electability.
Is there any wonder why most compromises out of Washington moves the country a little more toward the liberal belief in Socialism and why Liberals are always on the offence and conservatives are always on the defense.