He said May had done nothing but "double down on her own defeated deal", rather than seeking a compromise with lawmakers from all political viewpoints.
Speaking on BBC's The Andrew Marr Show, Mr Coveney assured that the backstop is not "dead", and said it is part of a "balanced package". Hancock then added: "It remains on the statute book but it isn't the focus of our attention".
With exactly two months left until Britain is due to leave the European Union on March 29, there is no agreement in London on how or even whether to leave the world's biggest trading bloc.
But he later suggested that he could be prepared to support it if the amendment had official Government backing.
There have been warnings that borders will be snarled up, hitting trade and leading to shortages.
Hancock said the pharmaceutical industry was doing everything it could to prevent shortages of medicines resulting from any delays at borders resulting from a no-deal Brexit.
If the Cooper amendment fails and this one passes, the pound could drop as much as 2 percent on a trade-weighted basis, according to Silberston. But she could lose it on Tuesday night.
The ministers are preparing to row behind plans to force May into accepting remaining within the EU customs union - a key demand of opposition parties.
He did say that the European Union would be open to looking at the political declaration between the United Kingdom and European Union again, and that the European Union would consider an extension to Brexit, with the United Kingdom set to leave on March 29.
The EU has said it will not change the legal text agreed with the UK PM.
In simple terms, MPs will vote to say whether the Prime Minister came to the Commons within three Parliamentary days of her historic defeat on the Withdrawal Agreement to set out her plan B - which she did.
Mrs May had urged MPs to back a different amendment that would propose "alternative arrangements" to the controversial Irish backstop plan, saying it would give her a "mandate" to secure a "legally binding change" in the EU.
Brussels, however, has insisted it will not reopen talks to amend the deal which has already been signed off by the other 27 European Union member states.
Two weeks ago, the Brexit withdrawal deal that concluded late previous year was comprehensively rejected by the House of Commons in an historic defeat for the government.
In a note of criticism of May's strategy, she said there appeared to be a lack of "ownership" in Britain of the agreement struck between the two sides in November, and that there was insufficient transparency in the prime minister's moves.
But one of the Prime Minister's most important negotiating weapons was ripped from her hands, as the House of Commons also voted to block a no-deal Brexit. The Brady amendment was supported by a majority of 16.
May wants lawmakers to support the proposal or amendment authored by senior Conservative lawmaker Graham Brady to call for the backstop to be removed and replaced with "alternative arrangements" during a series of votes, which are due to start at 2 p.m. ET.
In Northern Ireland, the DUP fear that the backstop could make the Irish Sea a de facto hard border between the United Kingdom and the island of Ireland, further isolating Northern Ireland. The amendment removes the contentious Irish backstop from the deal, setting May up for a clash with the EU.
"I think we should send the Prime Minister back to Brussels with a strong mandate to be able to say "If you compromise with us on this one issue, on the backstop, we would be able to a get an agreement - an agreement that is nearly there", he said.
This seeks to prevent a "no-deal" Brexit, something economists warn would be disastrous, by directing the government to extend the deadline if there is no agreement by February 26.