Expected Lords amendments to the Brexit legislation are set to return to the Commons on Wednesday.
Grieve was criticised in some newspapers over the weekend when he suggested he could "collapse the government" and said he woke up in a cold sweat thinking about it.
Tensions heightened after former attorney general Dominic Grieve warned that the Tory rebels he leads could "collapse" the Government if they disagree with the final outcome of withdrawal talks, and had the right to a proper say on Brexit.
Negotiations on a compromise, promised last week by May to avert a defeat, fell apart at the last minute on Thursday when rebels said the government had changed the wording of an agreement.
With no majority in the House of Commons, it take only a handful of Conservatives to vote against the government for May to lose. Wednesday's votes will be crucial for May's attempts to resist a "meaningful vote" plan that is seen as a step towards a softer Brexit - an outcome that would mean closer ties to the European Union on issues such as customs and regulations.
Mr Grieve also admitted that the amendment that will be debated this week had been watered down from its original version.
May and her senior Brexit ministers were eager to avoid words in the Brexit bill that would tie their hands in their negotiations with Brussels.More news: 'Quit separating the kids!' Trump faces Democratic rage on immigration
While Mrs May said she had been taking on board the concerns of her critics, but stressed the legislation must not restrict her freedom in the exit talks.
Leading backbencher Brexiteer Jacob Rees-Mogg said that the meaningful vote was being used to "obstruct Brexit" and "thwart the referendum result".
She said part of the?20 billion ($27 billion, 23 billion euros) injection would be funded by "the money we no longer spend on our annual membership subscription to the European Union".
They want Parliament to be given more powers if no deal is agreed, or if the agreement May makes with Brussels is deemed unacceptable by MPs.
Crucially, the motion will be unamendable, meaning that MPs can not insert a requirement for Mrs May to go back to the negotiating table, extend the Brexit transition or revoke the UK's withdrawal under Article 50.
One of May's mantras is that "no deal is better than a bad deal" and Brexit campaigners say Britain would lose one of its negotiating tools if the government can not threaten to walk away from the talks, which have all but stalled.
A paper laying out the UK government position, due to be published this month, has been delayed because the Cabinet can not agree on a united stance.