Greek Prime Minister Alexis Tsipras during the Economist Conference on "Europe: The comeback, Greece: How resilient?" in Athens on May 15. REUTERS/Alkis Konstantinidis Two cash crises are about to come to a head in Greece, with signals that both the financial system and the public coffers are about to run dry.

Athens barely made its latest payment (May 12) to the International Monetary Fund (IMF), and it managed to do so only when the government discovered that it could use a reserve account it wasn't aware of, according to the Greek media.

Kathimerini, a Greek daily newspaper, reports that Prime Minister Alexis Tsipras wrote to the IMF's Christine Lagarde warning that Greece would not be able to make that May payment, worth €762 million ($871 million, £554.2 million).

Pension and civil-servant pay packets are due at the end of the month, and based on this news Athens may struggle to pay them. Even if it does manage that, on June 5 the country owes another €305 million to the IMF.

In the two weeks following June 5 there are another three payments, bringing the June total to the IMF to over €1.5 billion.

Here's what's coming:

Greece may make some of its looming payments, but in June more than €1.5 billion is due to the International Monetary Fund. HSBC, Bloomberg, IMF, Business Insider

If Greece couldn't manage the €762 million payment in May without the IMF's reserve account, it seems likely that the government will struggle to make payments twice as large after another round of pension and salary payments.

But the public finances are not the only problem — pressure is building in the financial sector, too. According to Bloomberg, collateral is drying up there, and the situation also seems likely to meet a head in the next few weeks.

"The point where collateral is exhausted is likely to be near," JPMorgan Chase Bank analysts Malcolm Barr and David Mackie wrote in a note to clients May 15. "Pressures on central government cash flow, pressures on the banking system, and the political timetable are all converging on late May-early June"...

"We are in an endgame," ECB Executive Board member Yves Mersch said in an interview with Luxembourg radio 100.7 broadcast Saturday. "This situation is not tenable."

The government seems to have made little progress toward a deal to unlock the next tranche of bailout cash, too.

On Monday Greek newspaper To Vima reported a leak from the European Commission, suggesting that Brussels has blinked and offered Greece a relatively generous deal. But that doesn't mean that the individual European countries or the IMF will accept those compromises.

A leaked IMF document seen over the weekend by the UK's Channel 4 News confirms reports by Greek journalist Michael Ignatiou last week that while tentative compromises are in the making for a crucial bankruptcy law and some tax issues, there is still a gulf between Athens and its creditors on pensions and the labour market.

The document seen by Channel 4 describes the labour market as "the area where in the past most progresses were achieved." In short, it's no small speed bump for a deal, but a major roadblock. Without a solution, an agreement seems unlikely.

There's only one hope for the government at the moment. Figures from Kathimerini last week suggested the government had managed to drain about €600 million from local government and other state funds. That boosts the government's ability to pay, but it is far short of the €2 billion that it was initially suggested the move could raise. If the government manages to find more cash through similar methods, it could prolong the standoff.

But unless Athens can think of more and increasingly inventive ways to shake down the country to make these payments, it looks as if some form of default is looming.