The DUP leadership is said to have been "spooked" by the level of opposition to such an act, not only inside the party but in the wider unionist community.
"This is now a decisive phase of the process", she said.
The unsuccessful conclusion of the meeting was explained by DUP leader Arlene Foster to have been a result of a difference in opinions over a legislation for the Irish language.
She told Sky News: "I hope that the immediate next move is that the leaders of the DUP and Sinn Fein will keep talking to one another, to the Northern Ireland Secretary and that attempts to reach an accommodation will carry on".
Ms McDonald said her party warned the DUP to close the deal "before those opposed to it could unpick" it.
Civil servants have run the government in Northern Ireland since the administration collapsed, with major spending and policy decisions deferred.
O'Neill said she would be talking to the Irish and British governments and was to set out their position on the next steps on Thursday.
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Modi said the communist government sheds crocodile tears for labourers but did not grant them minimum wages. He said the CPI-M regime had developed complacency that they would never be ousted from the power.
The parties are also at loggerheads on how Northern Ireland should be governed if talks ultimately fail.
Britain's Northern Ireland Secretary, Karen Bradley, said in the absence of a Northern Ireland administration "other challenging decisions will have to be taken by the United Kingdom government".
Irish Foreign Minister Simon Coveney said the development was "very disappointing" and said he would be in close contact with the British government over the coming days to establish how to proceed.
The two parties blamed each other for the impasse that threatens power-sharing, the key achievement of Northern Ireland's 1998 peace accord that ended decades of bloodshed.
"As co-guarantors of the Good Friday Agreement, the United Kingdom and Irish governments have an obligation to uphold and protect the letter and spirit of that agreement", Coveney noted.
Amid the furore over the DUP's decision to pull the plug on the talks, of which May and her Irish counterpart, Leo Varadkar, painted an optimistic picture during their joint visit to Belfast on Monday, gay marriage campaigners attended Stormont on Wednesday. The rift soon widened to broader cultural and political issues separating Northern Ireland's British unionists and Irish nationalists.
Ms McDonald said the package included an Irish language act, an Ulster Scots act, and respecting language and diversity act. "Absolutely. When, I can not be sure", McDonald told reporters.