The battle over the residency rights of EU nationals in the UK will now head back to the House of Commons after peers voted 358 to 256 to defeat the government in the House of Lords on Wednesday night (2 March).
The timetable for the vote on the amendment to the Article 50 bill in the lower chamber will be decided by the House of Commons leader David Lidington.
Lidington held his weekly business session in the Commons on Thursday, but the senior Conservative failed to provide a date, with next week's Commons' business dominated by Chancellor Philip Hammond's so-called 'spring statement'.
The commons had already rejected granting unilateral residency rights to the estimated three million EU nationals in the UK, with just three Conservative MPs defying May over the issue.
The prime minster has consistently argued that she did not want to make the guarantee until UK nationals on the continent were afforded reciprocal rights. But the Lords' unwanted intervention may make more MPs think again.
However, May commands a majority of 16 in the Commons and has the support of the pro-Brexit and eight-MP-strong Democratic Unionist Party (DUP).
The PM will want to avoid legislative 'ping-pong' between the chambers after promising to invoke Article 50 and trigger Brexit talks by the end of March. If May missed her self-imposed deadline, she would likely face criticism from her pro-Brexit backbench MPs and Ukip.
"We are disappointed the Lords have chosen to amend a Bill that the Commons passed without amendment," a spokesperson for the Department for Exiting the EU said.
"The Bill has a straightforward purpose - to enact the referendum result and allow the government to get on with the negotiations.
"Our position on EU nationals has repeatedly been made clear. We want to guarantee the rights of EU citizens who are already living in Britain, and the rights of British nationals living in other member states, as early as we can."