That's exactly what happened in 1790, when the Founding Fathers overlooked their parochial interests - and defied their staunchest backers - by agreeing, for the good of the fledgling union, to put America's capital in a neutral place along the Potomac River.
Would the same outcome happen today? Fat chance.
In this polarized and partisan era, Washington careens from one crisis to the next even as the country faces huge problems that threaten its standing in the world. With power divided on Capitol Hill, bipartisan solutions are necessary. And yet, while both Democrats and Republicans talk a lot about compromise - a cross-the-aisle, solutions-driven approach - few seem willing to give ground to fix what ails the nation.
The latest example is the stalemate over deep budget cuts set to take effect Friday, absent a bipartisan deal. The cuts likely will inconvenience average Americans and may slow the nation's fragile economic recovery. Both sides are dug in on their ideological positions. President Barack Obama and his Democrats want more tax increases, while Republicans demand more spending cuts.
This is the fifth fiscal standoff since this period of divided government began in 2011, when Republicans took over the House while Democrats continued to control the Senate. In the other cases, both sides reached mini-deals to avert immediate crisis - only to ignore the larger issues. Skyrocketing debt and persistent deficits. Rampant waste, fraud and abuse. Budget-busting Social Security and Medicaid programs.
Why does Washington get so caught up this cycle of panic - whether manufactured or real - only to ultimately put a Band-Aid on the country's biggest gushers without ever mending the underlying wounds?
Politicians have little incentive to take the risk of working with the opposing party to reach solutions that will fundamentally fix a problem. They operate in a system that makes it hard to roll the dice because they're putting their own jobs on the line. Robust Republican and Democratic parties - and their conservative and liberal activists, whose voices drown out the centrist Americans seeking remedies - usually rebuke them rather than reward them.
"Rebels, risk takers and creative thinkers are marginalized early and are seldom promoted up the ladder of local/state/national politics," says David A. Drupa of the Society for Risk Analysis.
These days, he says, politicians seem to be allowing the short-term benefit for themselves - winning re-election - drive their decision-making, without getting far enough along in their return-on-investment analysis to examine the long-term benefit for the nation.
"They're trying to win the next battle, the next matchup, the next race, at all our peril," Drupa says.
Both parties promise to use their bank accounts to protect lawmakers who stick with their ideological positions, and punish those who don't. Deep-pocketed groups on the far right and far left also go after those deemed unfaithful.
At the same time, party leaders have proven extraordinarily successful in drawing congressional boundaries in a way that actually discourages House members from collaborating and all but ensures their re-elections if they don't. Most districts are stocked with hard-core Republicans and Democrats who typically will vote for lawmakers only if they demonstrate consistent party loyalty.
So the easy thing for lawmakers to do is just that. It's much harder to meet in the middle.
Thus, when Washington's players do end up compromising on the meaty matters, it's usually in a piecemeal way that kicks the larger problems to future generations. Those who dare to try to solve the big problems typically find they lack the juice, lose re-election or get so fed up with the gridlock that they retire.
All this is precisely what George Washington worried would happen if the country devolved into factions.
"He thought political parties would tear up the union and it wouldn't survive," says Willard Sterne Randall, a biographer and historian who has written several books on the Founding Fathers.
The first president's fear of factionalism was so great that he decided on a second term as Alexander Hamilton and Thomas Jefferson, whose political bases were businessmen and farmers, respectively, battled over competing visions for the union.
Yet while they differed, they also compromised when necessary - as they did during the "Dinner Table Bargain" that resulted in Washington becoming the nation's capital instead of New York, Philadelphia or elsewhere.
"They weren't at each other's throats politically. They could get together on a major issue," Randall says. "They wanted the union to survive, so they compromised where they had to for the good of it. That's the kind of tone there was. They were pragmatic idealists, and in Congress now, they are ideologues."
So how do we get back to those more reasonable roots?
The Democratic and Republican parties are strong, and they probably won't face serious threats from third parties in the near future. They certainly won't eliminate gerrymandering unless voters force it.
So maybe it's time for something radical, or at least radically reasonable. Maybe this is the moment for a few of the frustrated Americans in the middle - many of whom reject the extremes, complain about stalemate and fear for the nation's future - to take a risk.
What if they stepped forward as candidates with a promise that they'll do only what they think will solve the country's big problems, regardless of what it could mean for their political careers? What if they rejected the strict adherence to orthodoxy that party bosses demand? What if they promised to only serve one term, choosing explicitly to put the country's future over their own?
And then, by not going to Congress primarily to get re-elected, they just might end up with a surprising reward: getting re-elected.
Wouldn't the country - not to mention this supposedly neutral city on the banks of the Potomac - be better for it?
Liz Sidoti is the national politics editor for The Associated Press.