Members of the House of Lords are expected to vote in favor of an amendment that calls for EU citizens who are legally resident in Britain to be guaranteed the same status after the UK leaves the European Union.
Prime Minister May's government does not have a majority in the Parliament's upper house and the amendment to the Article 50 legislation is expected to secure enough support to pass, according to UK media reports.
In attempt to stave off the defeat, Home Secretary Amber Rudd sent a letter reassuring peers that the rights of EU nationals will be a top priority once negotiations begin.
The leader of the opposition Labour party in the House of Lords, Baroness Angela Smith of Basildon, said in an emailed statement to CNN that she was "deeply disappointed" in Rudd's move.
"To continue to use people as bargaining chips in this way is not only shameful but could have a dire impact on the UK's economy and essential services.
"Confirming the rights of those EU citizens living in the UK can only be of benefit to our citizens worried about their future in EU countries but the government's approach seems to be to sit back and wait for others to blink first."
The defeat in the House of Lords would set off a parliamentary back and forth. The amended bill would need to be sent back for consideration to the House of Commons, potentially endangering Downing Street's March 31 deadline to trigger Article 50, the formal start to the Brexit process.
The bill, which allows the UK government to trigger Article 50, was passed unamended in the House of Commons in February after MPs received conservative assurances of EU nationals rights' protections.
The debate on Wednesday begins at 3.30 p.m ET (10.30 a.m. ET) with the vote on EU nationals expected some time before 6 p.m.