As the country lurches closer to default, Yannis Varoufakis, the country’s flamboyant and polarizing finance minister, broke one of the key taboos over its debt crisis Thursday, calling for the rescheduling of two big debt repayments in July.

On July 20, Greece has to redeem bonds worth 3.46 billion euros ($3.95 billion), currently held by the European Central Bank. Within a month of that, it faces another similar redemption of €3.19 billion (for more details on the timeline of Greece’s debt repayments, click here.)

Increasingly desperate ad hoc measures have allowed it so far to meet all its obligations to its creditors–the country had to raid the cash reserves of public-sector organizations and even its own IMF holding account to meet a €775 million payment to the Fund earlier this week.

But the July repayments are of a different order of magnitude.

“It’s quite simple, these bonds must be pushed into the future,” Varoufakis told a conference in Athens. “This is clear also to the ECB,” he added.

For good measure, Varoufakis also complained about Greece being excluded from the ECB’s quantitative easing program.

Failure to pay the ECB would be disastrous in more than one way. In addition to the panic an actual default would cause by itself, it would make it impossible for the ECB to carry on lending to Greek banks against Greek government collateral through an emergency credit line. The banks would almost certainly collapse.

The government said earlier this week it’s still just running a primary budget surplus (i.e., before debt servicing costs). Over the first four months of the year, it scraped together a surplus of €2.164 billion. But the think-tank Macropolis points out that Athens effectively had to stop paying its bills to the private sector to achieve that. In March, the last month for which data are available, arrears rose 10% to €4.43 billion.

As such, Athens is only keeping up an appearance of solvency while it fights with its creditors over unlocking the last €7.2 billion of the 2012 bailout package. The two sides had hoped to agree tweaks to make the package more socially acceptable by the end of April, but the deadline was missed and a supposedly key meeting of Eurozone finance ministers also passed this week without any real progress.

No-one at the ECB was initially able to comment on Varoufakis’ call Thursday. Its Frankfurt headquarters were closed for the Ascension Day holiday, but President Mario Draghi will speak later in Washington, and will also meet with IMF managing director Christine Lagarde to discuss next steps. (Greece had also threatened to default on its payment to the IMF before finally coming round earlier this week.)

Ben May, an analyst with the think-tank Oxford Economics in London, says its chances of success with the ECB are extremely slim. Even in the 2012 bailout, which cost private investors up to 90% of their principal, the ECB was kept whole, he points out.

Reuters reported Varoufakis as saying that he wants the Eurozone to swap the €27 billion in Greek bonds held by the ECB for debt from the Eurozone’s specially-created bailout vehicle, the European Stability Mechanism, effectively shifting Greece’s debt off the ECB’s balance sheet while lengthening the repayment schedule.

But that would require parliamentary approval in many countries, which hawks such as Germany and Finland are unlikely to give.

“It’s a theoretical possibility but it looks very unlikely as it goes against the grain of everything that the Eurozone has been saying,” says May.