I don't know how you would get around infighting. Both parties pretty much disagree on everything. Asking the government to spend within its means is now considered "right wing," so limiting immigration to those who enter the country legally. Before the Johnson administration both parties agreed on those things. The Kennedy administration was the last real neo-liberal administration where both parties essentially agreed on things. Things changed under Johnson. He escalated the Vietnam War and the New Left in its various forms challenged his administration and then started its takeover of the Democratic Party. That led to the increased division of the parties.

In the early 1970s following Roe v Wade, Ted Kennedy, Bill Clinton, Al Gore and Jesse Jackson all made public statements renouncing the decision. Jackson called it "genocide" in public rallies. So why did they change? They all changed when they ran for president to get the approval of Planned Parenthood. Before then most Americans were in general agreement on abortion: they thought it was wrong except for extreme cases, such as the life of the mother.

Today, the parties are so far apart that I don't know how they can agree on anything. Look at some of the posters here as an example of what I'm writing about. If someone takes a reasoned point of view that disagrees with their point of view they leap out screaming "Fascist!" and "Racist!" and every other epithet they can think of, even to the point of sending out hateful pms. How do you reason with people like that? And if you can't reason with them, how are you ever going to find a point of agreement if there's a total lack of civility?