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Phewww! That's the White House on Scotland vote

Pro-union supporters celebrate as the Scottish independence referendum polling results are announced in Edinburgh, Scotland, Sept. 19, 2014.
Leon Neal | AFP | Getty Images
Pro-union supporters celebrate as the Scottish independence referendum polling results are announced in Edinburgh, Scotland, Sept. 19, 2014.

Scotland's decision to overwhelmingly reject independence from the United Kingdom brought great relief to a White House worried about the impact of a schism on several different fronts.

Had Scotland voted to secede, the fear was, U.K. politics would have been thrown into turmoil just as the United States was counting on its British allies to play a key supporting role in the campaign against the Islamic State in Iraq and Syria and continue to pressure Vladimir Putin in Russia.

Prime Minister David Cameron would have faced calls to resign and the nation's future in the European Union would have been called into immediate question.

So it came as no surprise that President Barack Obama greeted the results, which saw the "No" side win with a convincing 55.3 percent of the 2.6 million votes cast, very warmly.

"We welcome the result of yesterday's referendum on Scottish independence and congratulate the people of Scotland for their full and energetic exercise of democracy," Obama said. "Through debate, discussion and passionate yet peaceful deliberations, they reminded the world of Scotland's enormous contributions to the U.K. and the world, and have spoken in favor of keeping Scotland within the United Kingdom."

Obama added: "We have no closer ally than the United Kingdom, and we look forward to continuing our strong and special relationship with all the people of Great Britain and Northern Ireland as we address the challenges facing the world today."

Read MoreShocked by the Scotland vote? You weren't paying attention

It's not as though an independent Scotland would have ended the so-called special relationship between the U.K. and the U.S. Indeed, over the long term it would likely have drawn a smaller and more conservative United Kingdom even closer to its American ally.

But in the near term it would have distracted Great Britain at a dangerous time with Islamic extremists trying to reshape the map in the Middle East and Vladimir Putin harboring dreams of a return to empire in Russia. Other separatist movements in Europe, including in Spain's Catalonia region, might have draw significant momentum from Scottish independence.

"We are on these shifting plates in ways we have not seen since World War II," Jack Ablin, chief investment officer at BMO Private Bank, told me this week. "And Scotland is another stick that, if you move it, could potentially pull down this giant game of Jenga we are all playing."

Read MoreScottish nationalist leader quits after losing vote

In addition to the geopolitical fallout, Wall Street and Washington worried about the economic impact of a Scotland separation including both short-term market volatility and longer-term questions of the new nation's currency, debt load and EU membership.

Europe is already slowing and analysts say it would not take much to tip it into real recession with blowback on trade and overall confidence that could hit the U.S. as well.

The White House and congressional Democrats certainly did not want to go into the stretch run of the 2014 midterm elections with a European economic crisis possibly further crimping relatively slow growth in the U.S.

Now instead of headlines Friday morning about tanking markets and fears over the future of Europe, markets celebrated the Scotland vote and everyone was free to obsess over the initial public offering from China's dominant e-commerce company Alibaba, which raised $22 billion and immediately became one of the most valuable companies in the world.

The Obama White House did not openly campaign in favor of a "No" vote against Scottish independence. But there was never any doubt where the administration stood with the president and other officials stressing the need for a strong and "united" Great Britain.

Late polls suggesting a surge for the "Yes" side stirred other big Democratic names into action with former president Bill Clinton on Wednesday imploring Scottish voters to both show up in large numbers (which they did) and vote in favor of maintaining the union (which they also did).

Read MoreScotland's No vote: How it happened on Twitter

Scottish voters not only voted to maintain their ties to the U.K. but did so by a surprising 10-point margin that allowed Cameron to declare a "clear result" that should eliminate the question of independence for many years to come.

"There can be no disputes, no reruns—we have heard the settled will of the Scottish people," a triumphant Cameron said Friday outside No. 10 Downing Street.

Read MoreScotland votes No: Scenes of joy and despair

The mood in the White House was likely less jubilant. But probably not by much.

—By Ben White. White is Politico's chief economic correspondent and a CNBC contributor. He also authors the daily tip sheet Politico Morning Money [politico.com/morningmoney]. Follow him on Twitter @morningmoneyben.