But the US and Europe are waiting, too, and with no less a sense of expectation and concern. The country which was formed out of the ashes of Yugoslavia in a bloody conflict that ended only four years ago has shifted from being the apple of Washington's eye to the margins of polite diplomatic society. Not just the choice of new rulers, but a new political identity is at stake.
On Friday, the Speaker of the parliament, Vlatko Pavletic, stepped into the President's shoes and assumed his duties. A panel of judges ruled that the present incumbent was incapable of exercising his functions, and for an interim period, renewable every 60 days, Mr Pavletic will be in charge.
Franjo Tudjman and his party, the Croatian Democratic Union (HDZ), have dominated the new nation since it declared independence in 1991. A former military officer, Mr Tudjman had long been a critic of Yugoslavia, and he rapidly emerged as the strongman at a time of conflict.
The US backed him to the hilt, delivering military assistance and political support as he fought Serbian and Yugoslav forces. That culminated in Operation Storm, a deadly assault on the Croatian Serbs who lived in the Krajina. They were forced out of the country - those that were not killed. But soon after the war, relations cooled as Washington realised that the country's ruler was no Vaclav Havel.
Since then, Croatia has sat uneasily between the countries of Western Europe and its former partners in Yugoslavia, a devastated Bosnia-Herzegovina and a hostile Serbia. Its elections have been persistently criticised, and much of the media remains under the thumb of Mr Tudjman, the state and the party (which are hard to disentangle).
The government has failed to give full co-operation to the international war crimes tribunal and the country has failed to reincorporate the Serbs who fled during the war. In raids earlier this year, Nato troops seized evidence that its intelligence services had been deliberately destabilising ethnically Croatian parts of Bosnia-Herzegovina. Croatia is perilously close to being regarded as a rogue state.
So America and Europe will have heard a mixed message when Mr Pavletic, an academic and writer, set out his stall. "I must continue what the President would do," he said. He also said that the parliamentary elections "must be held in an atmosphere which will make clear to everyone that Croatia's democracy is mature and that no one will be able to deny the results".
Beset by factionalism and allegations of corruption, the HDZ should by all calculations suffer a setback on 3 January, to the benefit of the Social Democrats and Social Liberals. The economy has failed to take off and unemployment is around 20 per cent. Privatisation largely meant handing state assets to friends of the ruling party. But the opposition claims the choice of election date means there will be little campaigning. That is in line with the HDZ's systematic attempt to depoliticise politics and make itself Croatia's only option.
But Mr Tudjman is the keystone - without him it is unclear what will happen. No one has seen him since he was hospitalised on 1 November, but he is assumed to be close to death from the cancer he has fought for three years - yesterday doctors admitted his condition had worsened further. If he dies, a presidential election must be called.
After Tudjman, the party may not find it easy to unite on a successor. The sinister Ivic Pasalic, head of the intelligence services, may be a candidate and hardline deputy speaker Vladimir Seks is another possibility. The opposition, divided and inexperienced, may find it hard to unite on a candidate. It will be months, if not a year, before the nation's future direction seems clear.