Those who say there should be compromise are over-simplifying the problem and their ill-conceived solution. This is because a person of principle should never, ever compromise on a principle. Compromise has a place in ironing out details. But never in asking a person to betray their principles.
Example: Let's say one person is religious, another is atheist. One's religion says he must worship God every day, the other says we should not worship ANY day. A compromise would be, "OK, I'll worship on Tuesdays, Thursdays and Sundays only." That "compromise" is absurd - it solves nothing, makes no one happy and forces both to betray their beliefs.
But let's say that both are religious, and the debate is what date we should celebrate Easter. Since that is a detail rather than a principle (no one knows the date of the true Easter), they can compromise and choose a date that both can grudgingly accept.
The problem in Washington is one of opposing principles, not details. Ideally, both parties want the same thing, but bicker over the details. But that is not what we have. We have two diametrically opposed ideologies, just as we did prior to the Civil War. Back then, if the issue had been not whether or not we should have slaves, but rather how they should be treated, there could be compromise. But the issue was one of opposing principles, so compromise was not the answer.
If we want to break the gridlock in DC, the first thing we need to do is decide, as a nation, the direction we want to travel - a government-controlled nanny state, or a government controlled by and for the people. That is a core principle. Only when we consciously decide what kind of country we want can we then take the time to study the candidates for Congress and the White House, and vote not for a party, but for the people who will take us in our chosen direction. THEN we can have compromise on the details of how to get where we want to go.
Compromise is good, as long as it is not principles that are getting compromised. And whether or not the gridlock will cease depends not upon Congress, nor the President. It depends on US, making a choice as to what kind of country we want, and taking the time to become informed, and then vote.
For Thomas Jefferson was absolutely correct when he said, "Every person gets the government they deserve." If people do not keep informed, and research the facts, and act on it, then they do not deserve a government that will serve them as they would wish.