Greece’s finance minister on Monday authorized the transfer of 770 million euros to the International Monetary Fund, meaning the debt-saddled nation will meet this particular debt payment. But the Greek government will have very little fiscal liquidity for the month of May.  “This is absolutely the tightest it’s been,” says Douglas Elliott, a fellow at the Brookings Institution.

Athens will now hope to strike a new deal with European Union creditors that would unlock more bailout money without further tightening the screws on its battered finances. The country has approximately until the end of May or June until its newly-emptied coffers run dry. The question is: can Greece and the EU work out a new deal in time?

Germany’s finance minister has said he wouldn’t oppose a Greek referendum on the terms of such a deal, though the implication is that Greece’s left-wing Syriza government would be supporting its passage. If Greek voters were to reject the terms of a new E. U. deal, Greece would likely exit the eurozone. John Psarapoulos, a blogger for The New Athenian, says “what [Syriza] is entitled to do is negotiate a controlled presence of Greece within the eurozone. It is not authorized to negotiate an exit, even a controlled one.”

But even though Syriza has talked tough toward its EU creditors, it has moved to improve the country’s finances, says Vicki Pryce, chief economic advisor at the Centre for Economic and Business Research. “In other words,” Pryce says, “it’s improved its fiscal position a lot more than many other countries have done.”

So the EU may be moved by Greece’s efforts… or frustrated enough to take a tougher line.