Radio Television Serbia unofficially learned that Serbia has until 4 pm on Tuesday to decide on the proposal it was given in Brussels.
Hina learned from diplomats that the deadline was set because High Representative Catherine Ashton has deadlines for reports on negotiations between Belgrade and Pristina so that the European Commission can complete its progress report on Serbia.
The common assessment by politicians, observers and analysts in Serbia is that it would be disastrous for the country to reject the offer, said Tanjug news agency.
Prime Minister Ivica Dacic said dialogue was no longer possible because Pristina was set in its positions, adding that Serbia's state leadership thought the offer was poor and that they were making a decision "without any true friend in the West who would have understanding for our positions."
Deputy PM Aleksandar Vucic said Belgrade must try everything to get a date for the start of European Union accession negotiations, adding that the government was willing to make tough decisions and tough compromises.
He said Serbia was being forced to choose between two tough decisions, "accepting a very poor plan for Serbs in north Kosovo or refusing to sign any agreement."
The European Parliament's rapporteur on Kosovo, Ulrike Lunacek, has said that if Belgrade and Pristina fail to agree in the next couple of days, Serbia's window for the EU accession negotiations could be closed, according to Belgrade's media.
It is disappointing that despite Ashton's efforts, there has been no agreement, Lunacek told Vienna's Die Presse. She said the Serbs had not really opted for normalisation yet and hoped they would do so in the days ahead.
The media quoted Rainer Stinner, an official of the leading German Free Democratic Party, as saying that he saw no way in which Serbia could get a date for the EU negotiations and that there would be no solution as long as Belgrade tried to retain its structures in north Kosovo.
The biggest problem is that Serbia must accept that Kosovo was lost by former Serbian President Slobodan Milosevic, he told Danas daily ahead of a Bundestag delegation visit to Belgrade on April 10-11.
Serbian President Tomislav Nikolic's advisor Marko Djuric told Tanjug the state leadership would make a final decision on Brussels' offer after examining the losses in both cases, adding that "in both cases Serbia will be faced with big challenges and losses."
Djuric said the offer did not differ from the eight points made after the previous negotiating round in which Belgrade insisted on powers over the police, the judiciary and physical planning and that Kosovo's army should not be present in Serb-populated areas. He said those points did not mention any additional powers for the Serb community, security or legal guarantees, or the absence of Kosovo security forces in Serb-populated areas or at least in north Kosovo.
The deputy PM in charge of European integration, Suzana Grubjesic, said that refusing the offer would be bad for Serbia, isolating it politically and economically for a long time.
The Serbian Renewal Movement, which is led by Vuk Draskovic, a hardliner in the early 1990s and subsequently one of Milosevic's biggest opponents, is for accepting the offer from Brussels.