Peers are debating calls for the UK to protect the rights of EU citizens to remain in the UK after Brexit amid signs the government could be defeated.
Ministers say EU residents' status will be a priority once Brexit talks begin but opposition peers want a unilateral guarantee about their right to stay.
Lib Dems in the House of Lords say they expect a "clear victory" in a vote on an amendment to the Brexit bill later.
But Tory peer Lord Lawson said they were indulging in "virtue signalling".
Should the amendment be passed, it would be the government's first defeat on the bill - which will give Theresa May the authority to trigger Article 50 and begin official talks on the terms of the UK's exit from the EU.
If this happens, MPs could remove the Lords' proposed changes again when the bill moves back to the House of Commons later this month.
Home Secretary Amber Rudd, who was among ministers watching Wednesday's debate in the Lords chamber, has sought to reassure peers about the government's intentions, saying the 3.2 million EU nationals in the UK made a vital contribution and would be treated with the "utmost respect".
But she stopped short of offering a firm guarantee, saying this would not help the hundreds of thousands of UK citizens living on the continent as it could leave them in limbo if reciprocal assurances were not given by the 27 other member states.
The amendment, which would guarantee the rights of all EU citizens lawfully living in the UK at the time of the UK's departure from the EU, has cross-party backing.
Moving the amendment in the Lords, Labour peer Baroness Hayter said EU residents in the UK risked being used as "bargaining chips" in the negotiations and it was "in the gift" of the government to stop this happening.
While she was equally concerned about the two million Britons living on the continent, she insisted they should "not be traded against each other".
"These people need to know now, not in two years' time or even 12 months' time. They simply cannot put their lives on hold," Baroness Hayter said.
"Some are planning schools for their children, some are moving jobs, renting or buying a home or acting as carers. Some are receiving healthcare. Many more are working in our health service. All should have their uncertainty removed."
When will real showdown happen?
Parliamentary correspondent Mark d'Arcy
If there is ever to be a genuine parliamentary threat to the government's Brexit plans, when might it come?
The main pressure points are a bit further down the road… the first will come in the autumn when negotiations start in earnest, after the French and German elections are done.
At that point the EU will present its opening bid, which will probably be a demand for the UK to stump up a considerable exit fee. Will that provoke demands that the UK should throw up its hands and walk away from the EU then and there?
The battle lines on this are already beginning to form, with talk of legal advice on the enforceability or otherwise of any EU demands.
Earlier this month, MPs accepted assurances from ministers on the issue and passed the bill unamended but the government does not have a majority in the Lords.
Lord Newby, the leader of the 112 Lib Dems in the Lords, said passing the amendment would "require the Commons to think again".
The Lib Dems say they expected 230 of their own and Labour peers to vote for the amendment and for crossbenchers - the 178 independents peers who are not affiliated to any party - to back it by a margin of two to one.
One of these, former diplomat Lord Hannay, said he opposed the government's "transactional approach" and said his past experience of EU negotiations suggested a clear commitment at this stage would have a decisive impact.
But former Conservative chancellor Lord Lawson said that while he wanted to offer certainty to EU residents, he believed the amendment was "very foolish".
"At the end of the day, it will only hold up the bill for a day or two which is neither here nor there," he told the BBC.
"Everyone knows they (EU residents) are going to stay. Amber Rudd has made this clear, the view in the House of Commons is clear. There is no question of EU residents settled here having to go."
He added: "Basically it is virtue signalling, which is also the rage nowadays... coupled with the fact the opposition feels it has a constitutional duty to make life difficult for the government."
Former Tory leader Lord Howard said he backed a unilateral guarantee but the "unpalatable truth" was that neither the government nor the Commons would change their mind over the matter and the Lords should reflect on this.
And the Archbishop of York, the Right Reverend John Sentamu, said he opposed the amendment as it "neither revised nor improved the bill but added to it".
The moment to "shout as loudly as we can" about the issue, he argued, was once the UK had notified the EU of its intention to leave and proper negotiations began.
'Ping pong begins'
BBC political editor Laura Kuenssberg
Without a further more dramatic concession, the government are set to lose.
That will set in train the first 'ping' of the potential 'ping pong' - the parliamentary process where the Lords reject something in the red chamber, sending it back down the corridors to the green benches - daring, imploring perhaps, backbenchers to join with them and push back at the government.
There is no sign at the moment that ministers want to budge on this issue.
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The stages the Brexit bill needs to go through to become law:
(it is currently at committee stage in the House of Lords)