The last time the Congress was at work on a Sunday, it was last year when lawmakers were desperately searching for an agreement on a debt limit increase. In that case, political maneuvering ran right up to the midnight deadline.

And it is happening again now on the fiscal cliff.

As Senate GOP Leader Mitch McConnell left the U.S. Capitol on Sunday night, he still had phone calls ahead of him with Vice President Biden, as those two two men took charge of these tax and budget negotiations which so far have failed to produce a deal.

"There is no single issue that remains an impossible sticking point," McConnell said earlier in the day on the Senate floor, as he revealed that he had asked the Vice President - a former Senate colleague - to negotiate an agreement.

"I'm willing to get this done but I need a dance partner," said McConnell.

McConnell had been negotiating with Senate Majority Leader Harry Reid, but Reid stepped aside after McConnell complained that Reid and the White House had not responded to an offer that Republicans made just after 7 pm on Saturday night.

"There's still significant differences between the two sides," Reid said late on Sunday afternoon, "but negotiations continue."

The stumbling blocks were very familiar; where tax rates should rise in terms of income, how to deal with related issues like inheritance (estate) taxes, the Alternative Minimum Tax, extended long term jobless benefits and more.

There was also talk that the scheduled automatic budget cuts might not be altered at all by whatever scaled-back deal is cobbled together this week, dealing a dose of bad medicine to both parties.

Both sides lobbed the expected rhetorical bombs at each other through the day, each straining to gain the public relations edge on the other; meanwhile, the clock just kept ticking towards a midnight deadline on New Year's Eve.

Some though still held out hope of a bipartisan compromise.

"Whether we reach an agreement, today or tomorrow, or the next day after that, we will reach an agreement," said Sen. Tom Carper (D-DE).

Over on the other side of the Capitol, House members were sitting around waiting to see what the Senate might produce, with members of both parties unsure as to what they might be voting on - if anything.

"Until we know what we will consider, we just sit here and wait," said Rep. Dennis Ross (R-FL), who was waiting in front of a fireplace in the ornate Speaker's Lobby just off the House floor.

"We'll see how everybody reacts when the Senate does something," said Rep. Tom Graves (R-GA), one of a number of more conservative Republicans who might be candidates to vote against any deal that includes a tax increase on top income earners.

"I just don't think raising taxes solves the problem," said Graves, echoing GOP calls for more spending cuts that tax revenue increases.

The rare Sunday session - first since July 31, 2011 - had an odd feel from the start, as tourists filled the parking spaces outside the Capitol and jammed the hallways inside as Senators openly admitted they had no idea what was going to happen.

At one point, Reid told reporters he had sent the GOP a counter proposal, but then his staffers were forced to say that Reid was being sarcastic.

Most reporters missed the joke, quickly tweeting out the Reid news, but then had to pull that back a few minutes later as Reid's staff said there was no new offer.

The deadline for action is midnight - as the ball drops for the New Year - but no one would be surprised if the Congress is still battling away on January 1.

If there is no deal, about $100 billion in budget cuts would kick in along with tax increases on every working American.

Will lawmakers pull a rabbit out of the hat just as Americans watch the ball drop in Times Square?

Or will we go over the cliff and keep fighting about it in the New Year?

One thing is for sure, the Congress these days will use every possible day up until a deadline, and then some.