Greece’s anti-austerity government may think it’s being squeezed by its international lenders but that could be nothing compared to the pressure it faces from the country’s voters, experts warn.

The left-wing SYRIZA-led government under Prime Minister Alexis Tsipras has said it will not rush into a referendum or snap election to secure public support for the unpalatable reforms it may need to introduce to secure more funds. But analysts say neither can be ruled out as Athens desperately tries to avert bankruptcy.

Syriza, which came to power just a few months ago, is under public pressure to reach a deal with its creditors to unlock the last tranche of aid worth 7.2 billion euros ($8.2 billion) from a bailout program that expires at the end of June.

On Thursday, Greece offered a concession by agreeing to push ahead with the sale its biggest port, Piraeus, a cornerstone of the country’s important shipping industry, according to Reuters.

But reforms such as overhaul of the pension system demanded by Greece’s creditors – the European Union, European Central Bank (ECB) and International Monetary Fund — are unacceptable to Syriza’s left-wing supporters, putting Tsipras on a tricky path in what could be a crucial few weeks.

“Support for Syriza’s handling of negotiations with Greece’s creditors is starting to fall sharply and essentially if you ask me Greece is going to leave the euro zone this year, I would say emphatically no,” Nicholas Spiro, managing director at Spiro Sovereign Strategy, told CNBC.

“If you ask me ‘is Syriza going to complete its term in office?’ I would say at the very least it’s still entirely possible that a new election will need to be held,” he added.

“For the time being, Greek politics is the bigger risk than an outright Grexit.”

On Thursday, Greek Finance Minister Yanis Varoufakis suggested a debt swap to push back payments to the ECB would help Greece, but said that this could not occur because the idea filled ECB President Mario Draghi’s “soul with fear,” according to Reuters.

This week, Greece said it had emptied an IMF holding account to repay 750 million euros to the global lender on Monday – highlighting the grim state of the country’s financial position.

Economic data published on Wednesday meanwhile showed that the Greek economy, which last year escaped six years of recession, slipped back into negative growth in the first quarter as political turmoil took its toll.

“It is obvious that Syriza was elected into office with a strong mandate to push hard against the troika (of lenders), as such arguably, they have painted themselves into a corner and now they need to come out of that corner,” said Reinhard Cluse, chief European economist at UBS.

“And that means they need to make concessions and this will be very delicate from a domestic political perspective because they might lose credibility with their own electorate. It might expose the government’s own party to frictions,” he added.

Talks between Athens and euro zone negotiators have been deadlocked for months and analysts say time is now running out for the beleaguered country. A failure to secure a deal could precipitate a sovereign debt default and possibly Greece’s exit from the euro zone.

Mujitaba Rahman, an analyst at consultancy firm Eurasia Group, said in a note published two weeks ago that Tsipras may be able to win support for a deal by agreeing only partial pension reform in the weeks ahead.

But he added that the real test may come in June. By then Greece will need more funds and will have to introduce more comprehensive reforms, which many members of his government would find difficult to back. The option of a snap election, while ruled out by Tsipras, remained on the table, Rahman said.

Talk of a referendum to get public support for more austerity and allow Tsipras to keep his party together meanwhile has grown in recent days, especially after Germany suggested Greece may need to approve the harsh economic reforms creditors are insisting on.

“A referendum would allow the government to say credibly that this is not what we want but it’s what needs to be done to stay inside the euro zone,” said UBS’s Cluse.

Analysts said another option is to implement capital controls, which would keep funds within Greece. The last time capital controls were used in the euro zone was in the rescue of Cyprus’ economy in 2013. Then strict limits were placed on the amount of money that could be withdrawn and moved.

“That would be a face-saving way because Tsipras and Syriza want to stay in the euro without austerity but it’s hard to see how they would do that,” said Jim McCaughan, CEO at Principal Global Investors.