Ireland has launched a last-minute effort to warn Theresa May off any attempt to unravel the backstop, two days before a crucial Commons debate that may decide the next move for the UK’s rudderless Brexit policy.

Simon Coveney, the Irish foreign minister and deputy prime minister, insisted the backstop – the mechanism to ensure there will be no hard border between the Irish Republic and Northern Ireland if Britain and the EU fail to strike a free trade deal – was “part of a balanced package that isn’t going to change”. In a forceful interview, he insisted it was only part of the withdrawal agreement because of the UK’s red lines.

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On Tuesday Tory Brexiters may get the chance to vote for amendments that would signal their willingness to back May’s Brexit deal subject to the backstop’s either being removed or time-limited.

Ministers have not formally backed any of the anti-backstop amendments, which are incompatible with the deal that May agreed with UK leaders, but if one were to pass by a majority, she would be able to present the EU with a firm idea of what changes might get her deal through parliament – something that as yet remains unclear to Brussels.

MPs pushing the anti-backstop amendments will be competing against a rival bloc of parliamentarians hoping to get a majority for an amendment intended to prevent the government taking the UK out of the EU without a deal. Various versions of this are on the order paper, including some viewed with alarm by ministers because they cede control of the parliamentary timetable to backbenchers.

Facebook Twitter Pinterest Demonstrators hold banners in front of a mock wall on the Northern Ireland-Republic of Ireland border on Saturday. Photograph: Peter Morrison/AP

Last week there were reports claiming that dozens of pro-European ministers might resign if ordered to vote against the most robust anti no-deal amendment, tabled by Labour’s Yvette Cooper.

Those threats seem to have faded but, according to the Telegraph, pro-European ministers, including the work and pensions secretary, Amber Rudd, the business secretary, Greg Clark, and the justice secretary, David Gauke, held a conference call on Sunday night during which some of them said that the threat to resign could be reactivated if May did not bring a new deal back for a parliamentary vote within a fortnight. They fear that, if May is allowed to delay beyond the middle of February, a no-deal Brexit could become inevitable.

In an interview with BBC One’s The Andrew Marr Show, Coveney said he did not see the need for further compromise because “the backstop is already a compromise”. Although originally Northern Ireland-specific, it was made UK-wide at the request of May, he said.

“And the very need for the backstop in the first place was because of British red lines that they wanted to leave the customs union and single market,” he said.

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“So the Irish position is, look, we have already agreed to a series of compromises here, and that has resulted in what is proposed in the withdrawal agreement. Ireland has the same position as the European Union now, when we say that the backstop, as part of the withdrawal agreement, is part of a balanced package that isn’t going to change.”

Ireland has repeatedly stressed its commitment to retaining the backstop. But since May’s deal was rejected this month in the Commons by an unprecedented majority of 230, some ministers claim to have picked up signs that other members of the EU may be inclined to compromise on this in order to avert a no-deal Brexit.

Responding to Coveney’s interview, the health secretary, Matt Hancock, dismissed suggestions it had sabotaged May’s Brexit strategy for the coming week, saying all sides were looking for “pragmatic solutions” to the Irish border problem.

Hancock also played down a report claiming that, as part of government planning for a no-deal Brexit, officials had been looking at the possible need to introduce martial law to cope with civil disorder. Under the Civil Contingencies Act 2004, sweeping powers are available to the government for use in emergencies, but Hancock said that, while governments have to look at all options, martial law was “not specifically” being looked at.

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In a further development on Monday the Commons Brexit committee published a report suggesting that the government was being too complacent about how the negative consequences of a no-deal Brexit might be contained.

“While the EU might agree to side deals to mitigate the worst of the disruption of a no-deal outcome, this cannot be guaranteed, and we are concerned by the extent to which assumptions of an ongoing cooperative relationship underpin the government’s no-deal planning,” said the report, which was approved by a majority of the committee after five Brexiter members voted against.

“Since these assumptions cannot be guaranteed, a ‘managed no deal’ cannot constitute the policy of any responsible government,” the report went on.

Hilary Benn, the Labour MP who chairs the committee, said: “Having taken a wide range of evidence on the implications of a no-deal Brexit, the committee is clear that this cannot be allowed to happen.

“It would disrupt supply chains, create costs and uncertainty for businesses, threaten the reintroduction of tariffs and new non-tariff barriers which would affect competitiveness and many small businesses are not ready because they don’t know what to plan for.”