Bosnia-Herzegovina's federation reflects the political setup of the country and its ethnic division after the 1992-95 war. It consists of two associations: one a Bosnian Serb and another shared by Bosniaks and Bosnian Croats.
Together they are headed by a three-member presidency, made up of a Bosniak, a Croat and a Serb.
Just like in politics, the Bosnian Serbs do not agree with the concept of one president because they fear it might jeopardize their autonomy. All Bosnian Serb delegates and a number of Bosnian Croats voted against the change.
Bogdan Ceko, the head of the Bosnian Serb association told media after the meeting that he "does not feel personally responsible for this but we can talk about a collective responsibility." Bosnian Serbs base their refusal on the country's constitution written in 1995 during peace negotiations in Dayton, Ohio.
The peace agreement ended the Bosnian war but divided it along ethnic lines and prescribed a three-member presidency for the country - a setup that has proven ineffective as all three have to agree in order to pass a decision.
The three-member presidency and other provisions of the Bosnian statute that did not conform to FIFA's standards were tolerated for years because both FIFA and UEFA were aware of Bosnia's political problems.
But in October last year, both agencies told Bosnia that 15 years after Dayton the transition period is over and that if the country does not conform to the rules by end of March, it will be suspended. Back then, the Serbs said they won't change the current setup but that the three presidents can rotate as chairman every 16 months.
A suspension would effectively punish those in Bosnia who voted for FIFA's and UEFA's rules and will reward those who voted against them because people in the Serb half of the country don't even support Bosnia's national team.
They view the national team of neighboring Serbia as their own, and would not be unhappy to see the Bosnian team suspended.
"It's hard. I'm taking this very hard," said Muhidin Rascic, a Bosniak member of the federation's executive board. "Only I know how much of my life I have invested into all of this and now it's gone." Bosnia's suspension from world football would have to be confirmed by the emergency committees of FIFA and UEFA chaired by their respective presidents Sepp Blatter and Michel Platini.
FIFA said Bosnia "will be suspended with immediate effect" if Thursday's deadline for change passes.
Suspension from world football prevents a country's national and club teams, and its referees, from taking part in international matches. Officials are also excluded from international football business, while funding from the world and European governing bodies is frozen.
FIFA and UEFA met with Bosnian clubs last month to explain the consequences of a suspension.
"They do not want to be victims of people who do not want to take care of the future of football," FIFA said Tuesday in a statement.
In the national league standings, Borac Banja Luka from the Serb region has an eight-point lead and faces being denied a first entry into UEFA's Champions League competition next season if no compromise is reached.
If not solved in the next two months, the dispute could damage Bosnia's promising prospects of qualifying for the 2012 European Championship.
Its next international qualifier is June 3 away to Romania, which it beat 2-1 in Zenica last Saturday. Bosnia is scheduled to host Albania on June 7.
The matches could still go ahead if Bosnia backs down and meets the demands of FIFA and UEFA.
If the stand-off continues, Bosnia would lose the right to attend the FIFA Congress on June 1 in Zurich, where up to 208 national associations are scheduled to vote in the FIFA presidential election.