By Gabriel Gatehouse
BBC News, Kiev
Opinion polls suggest Nato membership is not widely supported
Just hours before President George Bush's plane landed at Kiev airport, protesters were busy burning his effigy outside the US embassy.
Thousands also rallied in the Ukrainian capital's main square, protesting against the Ukrainian government's plans for closer integration with Nato.
"We don't want Nato", said one protester. "We don't want our country to be dictated to by any other country. I want my children and grandchildren to live in a free Ukraine."
This is a widely held opinion. A recent poll suggests that 50% of Ukrainians want their country to stay out of Nato. If a referendum were held tomorrow, only around a quarter would vote to join.
More often than not, though, when you ask people why they are so opposed to Nato membership, they talk not about Ukraine, but neighbouring Russia.
"If you're dealing with a neighbour that has about the same amount of trade with Ukraine as the European Union", says Konstantin Grishenko, foreign affairs spokesman for the opposition Party of the Regions, "you don't poke something into his eye".
And it is not just trade that Ukrainians worry about. Recently, Russian President Vladimir Putin suggested that Russia might re-aim its missiles at its neighbour, if Ukraine were to host Nato bases on its territory.
So, to counter a largely negative image, Nato is conducting a low-key PR campaign in Ukraine. From its small Kiev office inside Taras Shevchenko University, it supports events that promote a "better understanding" of the alliance.
Ukrainian soldiers are deployed in Afghanistan, Kosovo and Iraq
At one such recent event, an Estonian delegation came to talk to students of international relations. Estonia is, like Ukraine, a former Soviet nation - but it joined Nato in 2004.
So, says former Estonian Defence Minister Sven Mikser, Ukraine has nothing to worry about.
"Even today, if you ask a Russian politician, he or she would say they're not happy about Estonia being a member of Nato.
But I think they've learned to live with the fact quite well.
"Fundamentally, I think that most Russian politicians are pragmatists - they understand the things they can influence and change and the things they just have to learn to adapt to. And Nato enlargement is one of those things."
But Ukraine is of far greater strategic importance to Russia than Estonia. Yana, one of the students in the audience, certainly was not reassured.
"I am convinced there will be problems with Russia, especially given our dependence in the energy sphere. And I doubt that Nato member states would provide us with real support in the political sense."
Colonel Boris Kremenetsky is in charge of Nato integration for the Ukrainian armed forces. Twenty years ago he was in Afghanistan, flying bombers for the Soviets.
These days, there are still Ukrainian military personnel in Afghanistan, but now they are under Nato command.
The same goes for Iraq and indeed Kosovo, where Ukraine has a contingent of 182 peacekeepers.
Col Kremenetsky says that Ukraine does a lot more for the alliance than some Nato members.
"If we are talking about pure military, we were ready to join yesterday, according to our contribution so far, according to the capabilities we have."
The government also believes it is time for Nato to show some reciprocation. "We need clarity," says Boris Tarasyuk, a former foreign minister and now a pro-government MP.
By that he means a decision at Bucharest to invite Ukraine to join Nato's Membership Action Plan, or MAP.
And at stake, he believes, is nothing less than the sovereignty of Ukraine itself.
"The positive decision on Membership Action Plan to Ukraine will finally stop speculation in neighbouring Russia whether Ukraine can still be the subject of domination or not."
So on one thing both sides agree: at stake here is the issue of Ukrainian sovereignty itself. For the government, the ambition to join Nato is about far more than just replacing outdated Soviet military hardware.
It would, ministers believe, cement Ukraine's independence as a nation and allow the country to move out of Russia's shadow. But before they get there, they have got a lot of persuading to do, both at home and abroad.
You can hear Gabriel Gatehouse's radio report on the World Tonight on BBC Radio Four, Tuesday 1 April at 2200 (2100 GMT)