A United Kingdom -- but for how long?

LONDON -- London is the indisputable center of the British political universe -- especially on a Wednesday, when the party leaders try to tear strips off each other in the made-for TV spectacle that is Prime Minister's Questions in parliament.

Not this Wednesday, however.

CBS News correspondent Mark Phillips reports that the leaders of all three major U.K. political parties have traveled north to Scotland to deliver a political love-bomb, to try to keep the United Kingdom united. It's genuinely that serious.

When you think of Scotland, what do you think of?

Bagpipes? Kilts? Perhaps strange Highland sports like flipping logs, or even curling? Or the obvious golden-brown single malt beverage for which the country is renowned?

Think again.

Scotland is in the middle of a referendum campaign on whether it should break away from the rest of the United Kingdom and become an independent country. And in just the last week, the polls have tightened to the point where the vote is now too close to call.

According to the polling, the momentum has shifted toward separation, and that is precisely why Britain's political leaders, including Prime Minister David Cameron, have headed north.

"I want them to know that the rest of the United Kingdom -- and I speak as Prime Minister -- want them to stay," said Cameron recently.

Cameron's problem is that as the posh, southern leader of the Conservative or "Tory" pary, he's seen in Scotland as the personification of everything that's wrong with England and the U.K.

Pro-independence leader Alex Salmond calls today's campaigning by Mr. Cameron a gift, and a sad and desperately given one at that.

"If I thought they were coming by bus," quipped Salmond, "I would send their bus fare. This is a fantastic boost for the 'yes' campaign."

The Yes campaign has been playing on Scottish nationalism -- on its desire to control its own affairs.

The No's say choosing independence would be a leap into the unknown -- including basics such as not knowing what currency the new country would even use.

It's so close now that Queen Elizabeth II -- who is in Scotland this week and is supposed to be above politics -- is said to be very concerned that a country which has held together for 300 years may be breaking apart on her watch.

The palace has had to issue a statement making it clear she will not enter the very public debate.

But other big names have, including President Obama.

"We obviously have a deep interest in making sure that one of the closest allies that we will ever have remains a strong, robust, united and effective partner," Mr. Obama said in June.

As the polls show, that is now in serious doubt. The vote is next Thursday, and the outcome is anyone's guess.