Inside the cozy enclaves of GOP bonhomie—hunkered at the tables of see-and-be-seen Washington restaurants—Republican leaders are sourly predicting a party-busting independent presidential bid by a tea-party challenger, like Sen. Rand Paul, R-Ky., in 2016.

To them, the GOP apocalypse looms larger than most realize. Dueling State of the Union rebuttals and Karl Rove’s assault on right-wing candidates are mere symptoms of an existential crisis that is giving the sturdiest Republicans heartburn.

And yet, the heart of the matter extends beyond the GOP. My conversations this week with two Republican officials, along with a Democratic strategist's timely memo, reflect a growing school of thought in Washington that social change and a disillusioned electorate threaten the entire two-party system.

(RELATED: 6 Reasons Why the Two-Party System May Become Obsolete)

Seem like a lot to swallow? Allow me to describe my last few days at work.

Between bites of an $18.95 SteakBurger at the Palm, one of Washington’s premier expense-account restaurants, Republican consultant Scott Reed summed up the state of politics and his beloved GOP. “The party,” he told me, “is irrelevant.”

He cited the familiar litany of problems: demographic change, poor candidates, ideological rigidity, deplorable approval ratings, and a rift between social and economic conservatives.

“It’s leading to some type of crash and reassessment and change,” said Reed, who ran Bob Dole’s 1996 presidential campaign and remains an influential lobbyist and operative. “It can’t continue on this path.”

Reed sketched a hypothetical scenario under which Paul runs for the Republican nomination in 2016, loses after solid showings in Iowa and other states run by supporters of his father (former GOP presidential candidate Ron Paul), bolts the GOP, and mounts a third-party bid that undercuts the Republican nominee.

Paul, a tea-party favorite who was elected to the Senate in 2010, told USA Today on Wednesday that he was interested in running for the Republican presidential nomination in 2016. "I do want to be part of the national debate," he said.

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What are the odds of Paul or another GOP defector splitting the party? Reed asked me to repeat the question—and then grimaced. “There’s a real chance,” he replied.

The next morning, Rep. Reid Ribble of Wisconsin dipped his spoon into a bowl of strawberries, sugar, and pink milk—and declared the era of two major parties just about over. “I think we’re at the precipice of a breakdown of the two-party system,” said the Wisconsin Republican.

Voters are tired of partisan rancor and institutional incompetence, Ribble said, pointing to polls that suggest the number of independent voters is rising.

“Ross Perot was a goofy guy,” he said of the deficit hawk who mounted two independent presidential bids in the 1990s. “If he was packaged as a different guy and had the Internet, he would have emerged [as president]. The warning bell he was sounded then is getting louder today.”

(Related: In Congress, Compromise is a 4-letter Word")

Ribble represents one of the few House districts still divided almost equally between Republican and Democratic voters. Many of the rest are gerrymandered, drawn to easily elect a conservative Republican or liberal Democrat. It's one cause of gridlock, what voters loathe about Washington. “I think over a period of time we could watch third and even fourth parties emerging,” Ribble said.

A third voice joined the conversation when Democratic consultant Doug Sosnik released his State of the Union memo, a remarkable document warning both Democrats and Republicans about the increasing likelihood of a third-party presidential bid.

“And even though the Republican Party is in free fall, the Democratic Party’s position among the electorate has only marginally benefited from its misfortune,” Sosnik wrote. “The broad sense of alienation leaves a very wide door open for a third party presidential candidate in the future.” (Disclosure: I coauthored a book with Sosnik and GOP consultant Matthew Dowd about the effect that social change has on politics.)

Sosnik noted “the staggering pace of economic, demographic, and technological change,” a period of social tumult that rivals the first years of the industrial revolution. “All the upheaval and uncertainty have taken a toll on Americans’ confidence in their government and institutions to solve the nation’s problems,” Sosnik wrote, touching on a topic I explored in a 2012 National Journal magazine feature, “In Nothing We Trust.”

“This disaffection shows no signs of dissipating any time soon,” Sosnik continued. “There’s little doubt that it will continue to be a major challenge for both political parties and future presidential aspirants as the clock continues to tick on President Obama’s presidency.”

In a telephone interview last week, Sosnik said voters are wary of the leadership pool in U.S. politics. Business or even religious leaders could find traction in future presidential races.

“I think we will have a great debate with third and even fourth parties” vying for traditional GOP voters as well as Democrats now aligned with Obama, he said.

The Democratic Party will have trouble transferring Obama’s popularity to its next presidential nominee unless Hillary Rodham Clinton runs, Sosnik told me.

“I’m not surprised Republicans in this town are telling you they’re worried about the declining influence of their party and the potential for a third-party bid,” Sosnik said, adding with a chuckle: “Democrats should worry, too.”

He wasn't joking.