Two days out from the end of the year, lawmakers appeared to have made little progress toward devising a compromise to keep the nation from going over the so-called fiscal cliff at the start of 2013. All eyes were on the Democratic and Republican leaders in the Senate, who vowed to keep chipping away despite the wide gulf still separating them.

President Barack Obama exhorted lawmakers on Saturday to work hard for an accommodation. But earlier, optimistic words from the Senate’s top Republican, Mitch McConnell, were muted by this cautionary note from the top Senate Democrat, Harry Reid: “Whatever we come up with is going to be imperfect.”

A look at why it’s so hard for Republicans and Democrats to compromise on urgent matters of taxes and spending, and what happens if they fail to meet their deadline: