WASHINGTON — If there is a rock bottom in the frayed relationship between Senate Republicans and Democrats, it seemed uncomfortably close as the final days of 2013 on Capitol Hill degenerated into something like an endurance contest to see who could be the most spiteful.

As the sun rose on Friday, senators had worked through a second straight late-night session — called by Democrats as a way of retaliating for Republicans’ delaying tactics on confirmations. They held their first vote of the day at 7 a.m., confirming Deborah James to be secretary of the Air Force. And absent a compromise, they may still be voting through Saturday, a prospect that has thrilled no one.

“I think it resembles fourth graders playing in a sandbox, and I’ll give the majority leader, Harry Reid, 99 percent of the responsibility for it,” Senator Lamar Alexander, Republican of Tennessee and usually one of the more reserved members, said Thursday.

“He’s going to have ‘The End of the Senate’ written on his tombstone,” Mr. Alexander complained.

Senator Richard Blumenthal, Democrat of Connecticut, called this week “chaotic and confusing, and a shameful waste of time.”