To many Americans, what’s going on in Washington looks like a circus show that isn’t the least bit entertaining — the nation’s leaders seemingly unable to come up with a deal that keeps most people from paying higher taxes.

But there is a logic to it. For all the posturing of the last few weeks, both sides see a measure of political upside in going over the “fiscal cliff” — or, at the least, an advantage in waiting until the last minute, since they want to avoid drawing the ire of their most loyal supporters by appearing to cave too quickly.

“This is a town where each side seems to see a political advantage to their position when nothing is happening,” said Sen. Ben Nelson (D-Neb.), who will retire Thursday and cautioned his colleagues against leaving the tricky negotiations for newcomers who will take office in a few days. “There’s enough blame to go around.”

Late Sunday, Vice President Joe Biden and Senate Minority Leader Mitch McConnell (R-Ky.) were engaged in high-stakes, last-minute talks on a deal that would avert the most significant economic effects of the fiscal cliff. There remained hope on Capitol Hill that a breakthrough could lead to votes in the House and Senate on Monday, ahead of a midnight deadline.

Lawmakers said they were deeply frustrated — even disgusted — by the spectacle of the lurching talks. But they said they have become resigned to last-second dealmaking in a divided Congress.

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“It’s under the crucible of a time constraint that this place acts,” Rep. Scott Rigell (R-Va.) said.

For both parties, there are some logical incentives to go over the cliff.

Democrats are fresh off electoral victory in November and fighting a reputation that they too easily give ground. The way they see it, they’ll get what they want no matter what. Either they get a deal that includes tax increases on the wealthy or they go over the cliff. At that point, taxes would go up for everyone, and the Democrats would immediately move to cut rates for all but the wealthy.

They may, in fact, get more of what they want by waiting. As of late Sunday, for instance, Democrats appeared willing to agree to raise rates only for those making more than $400,000. But if they go over the cliff, Democrats would have less need to negotiate and could seek to set that number at $250,000, their original goal.

Sen. Patty Murray (D-Wash.) on Sunday reiterated a view she has pressed repeatedly with her Democratic colleagues: Going over the cliff is better than agreeing to a bad bargain. “We can’t accept a bad deal just because we’re here,” she said. “We have to keep working to get a good deal.”

Deal or no deal, the longer the current dynamic lasts, the longer Democrats will seek to portray Republicans as beholden to the rich at the expense of the middle class.

“They say that their biggest priority is making sure that we deal with the deficit in a serious way, but the way they’re behaving is that their only priority is making sure that tax breaks for the wealthiest Americans are protected,” President Obama said Sunday on NBC’s “Meet the Press.” “That seems to be their only overriding, unifying theme.”

Republicans, who control the House and still maintain a good bit of power in Washington, also see the merits of going over the cliff.

Not voting for a deal means not voting for a tax increase, which has been a central tenet of the party for more than two decades. Many Republican lawmakers are loath to give up their purity on the issue, in part because they are more concerned about a primary challenge than their standing in national opinion polls.

If they go over the cliff, they, too, could quickly move to cut taxes. In the meantime, they would seek to blame President Obama and other Democrats for the largest tax increase in generations.

Many Republicans also believe they can get a better deal with Democrats in an upcoming debate over the nation’s debt limit. In about two months, the government will no longer be able to pay its bills unless Congress takes action to raise the limit on federal borrowing. Many in the GOP think that deadline gives them the upper hand.

While taxes are the main battleground, both sides see some value in allowing deep spending cuts to occur, too. Many Democrats believe defense spending could be trimmed, while many in the GOP are happy to see domestic spending cut.

Still, while the two sides may see value in waiting to the last minute or going over the cliff, there are ample risks for both Democrats and Republicans.

Americans are not likely to be pleased by any more Washington dysfunction, particularly if financial markets react poorly and the country is ridiculed around the world. While opinion polls indicate that most of the blame, at least initially, would be directed at Republicans, the president remains the steward of the nation’s economy, and at some point dissatisfaction would likely turn his way.

Obama also has a number of other critical domestic policy initiatives — on immigration and gun control, for instance — that he is eager to get to and will need at least some support from House Republicans to pass.

On Sunday, members of both parties lamented their own actions — or lack thereof.

“It looks awful. I’m sure the American people are saying, with so much at stake, why are they waiting so late to get this done? And I’ll tell you, it’s human nature,” said Sen. Richard J. Durbin (D-Ill.). “When it’s something painful, we put it off to the last minute, and this is a pretty painful exercise.”

Outside observers said it was inevitable that lawmakers would put one foot over the cliff, if not jump completely.

“It was always going to be very hard to get any sort of big deal before going over the fiscal cliff,” said William Gale, a tax expert at the Brookings Institution. “The reason is that Republicans would have to vote for a tax increase to have that happen. And they’re just not going to vote for a tax increase.”

Kevin Hassett, an economist at the conservative American Enterprise Institute, argued that Democratic strategy has always been to go over the cliff. “It increases their political leverage,” he said. “To make that work, of course, they need to pretend not to want to, but I think that is their play.”

Staff writer Ed O’Keefe contributed to this report.

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