In a loosely coordinated strategy, the EU's top officials, European Council President Herman Van Rompuy and European Commission President Jose Manuel Barroso, have telephoned Greek party leaders in recent days to spell out that if Greece wants to stay in the euro it must abide by the terms of the EU/IMF bailout, several sources said.
German Chancellor Angela Merkel, her finance minister, Wolfgang Schaeuble, and other influential voices such as European Central Bank executive board member Joerg Asmussen have delivered the same message publicly
European leaders have concluded that Greece will need a second election and aim to apply enough pressure on politicians and voters by then to engineer a majority in favour of Athens' bailout. Privately, European Union officials are alarmed at the potential turmoil for the euro currency area if Greece were to tear up its austerity programme and default on its debt.
"Certainly we are very aware of the seriousness of the situation and we are delivering our message very firmly,» said one EU official involved in coordinating the calls. «We are not the only ones. The message is coming from everywhere."
As well as leaving Greek politicians in no doubt as to the devastation the country would face, the aim is to shock Greek electors into turning a second round of polling into a vote for or against the euro, producing a clearer result.
Opinion polls show 75-80 percent of Greeks want to stay in the euro. The calculation is that the desire to retain the currency will ultimately trump opposition to the bailout.
If faltering efforts to form a coalition fail, as appears increasingly likely, another parliamentary election could be held as soon as mid-June, with most estimates suggesting June 17 as the date.
That leaves around a month for Brussels and other capitals to press the message on Athens and the Greek people.
Schaeuble, a stern critic of Greece over its failure to meet its bailout targets, defined the choice in crystal terms during a visit to Brussels on Wednesday, saying that if the country wanted to keep the euro it had to stick to agreed reforms.
He also reversed the psychology, saying that if Greece wanted to leave the currency union, there was little that could be done to stop it. That echoed language used by Merkel and outgoing French President Nicolas Sarkozy in November last year, when Greece also appeared close to leaving the euro zone.
"If Greece decides not to stay in the euro zone, we will not be able to force it,» Schaeuble said, pointing out that Asmussen had made similar comments. «That is nothing new."
The official line is that there can be no renegotiation of the bailout programme, which was only adopted finally in February. But privately, some Brussels officials are calculating how much more funding Greece might need if its targets were pushed back a year to soften the austerity a little.
The euro zone applied firm financial pressure on Athens on Wednesday, with the European Financial Stability Facility, the 700 billion euro fund being used to finance Greece's second bailout, withholding a portion of the next scheduled payment to Athens.
While there was no suggestion that the decision was coordinated or linked to the political pressure being exerted, the board of the EFSF, made up of representatives from the 17 countries in the euro zone, agreed to disburse only 4.2 billion euros of a planned 5.2 billion euro payment to Greece.
"The remaining funds of 1.0 billion euros are not needed before June and will be disbursed depending on the financing needs of Greece,» the EFSF said in a statement.
The head of the fund, Klaus Regling, turned the screw further on Thursday, saying no money beyond that would be paid to Athens until inspectors from the European Commission, European Central Bank and IMF have had a chance to visit.
The next visit of the three organisations, together known as the troika, was expected in June, but is now unlikely to happen until there is a new Greek government in place.
The ultimate aim of the EU's pressure is not only to ensure that a government is formed in Athens and that it sticks to the bailout programme, but that the country honours its obligations to its creditors, most of whom are now euro zone member states.
Any risk of Greek default or of the country leaving the euro zone - which would be a de facto default - will have an immediate impact on the finances of most other euro zone states.
"After the private-sector writedown, we are even more stuck with Greece than before, because if they default, they default to us,» said an EU official involved in debt negotiations.
"Tactically, it makes sense to frame the choice as either you deliver or you're out. But in substance, it can't be framed that way because we can't afford to lose Greece."
The goal therefore has to be to exert pressure without pushing Greece over the edge, which means emphasising the benefits of euro zone membership while firmly underlining the obligations to the bailout for the good of the country.
If Greece can't stick to its second bailout - having already failed to meet the demands of the first programme agreed two years ago - there will be no third chances, officials insist.
"If they cannot implement the programme, they will default,» said a third EU source. «I just don't see that the politics will be there for creditor states to open their wallets again.»