Northern Ireland Office minister Lord Caine said the Bill “will help to plug the governance gap” in the region, but insisted it was not a long-term solution.
The post-Brexit arrangement has created economic barriers on the movement of goods from Great Britain, causing resentment and anger among many unionists and loyalists.
The Bill aims to buy further time for negotiations with the EU over the protocol.
Speaking in Parliament, Lord Murphy said: “The Bill we accept. We don’t welcome it. It reflects the dreadful situation in Northern Ireland at the moment which has to be addressed.”
On the executive formation deadline, he told the upper chamber: “They can’t do it in seven weeks. That’s absolutely the case. Frankly, I think it’s a bit daft to put a deadline of seven weeks. I don’t understand the logic behind it.
“There’s Christmas in-between. For at least two probably three weeks nothing but nothing will happen.
“I really would urge the Government to think a bit more about that January 19 deadline.
“Unless it’s a clever ruse which I don’t think it is, then I rather suspect it needs to be rethought.”
Liberal Democrat Lord Bruce of Bennachie said: “The timescale is tight to the point of being unrealistic.”
He proposed an amendment to remove the deadline and give the Northern Ireland Secretary the power to set a date instead, but later withdrew it.
Lord Caine said: “Clearly, we hope the time period afforded by the legislation will create the space required for talks on the protocol to make some progress.
“But it is not and never has been the intention in this legislation to create an indefinite or undefined extension to the executive formation period.
“I do not think it would be appropriate to have an open-ended delay to that deadline.”
He added: “Sadly, this Bill is a regrettable necessity.”
Earlier, former SDLP leader Baroness Ritchie of Downpatrick said: “To me, this legislation represents not only a further manifestation, sadly, of political failure but is also the Secretary of State putting a sticking plaster on a running sore of ongoing political paralysis in Northern Ireland.”
Making his maiden speech in the Lords, DUP peer and former education minister in Northern Ireland Lord Weir of Ballyholme said: “We should be in no doubt that not only is the Northern Ireland Protocol the root cause of this legislation, but – although it is not directly mentioned in the legislation – it remains the elephant in the room when we are discussing it.”
He added: “It would be a misconception to believe that any level of reduction in or promise of restoration of pay will have any great impact in changing the principled position that my party and others have on this issue.”
Former deputy DUP leader Lord Dodds of Duncairn said he “reluctantly” welcomed the Bill.
“It is necessary but unfortunate,” he added.
Fellow DUP peer Lord Hay of Ballyore said: “Although limited in nature, the Bill allows the negotiations the space to find urgent solutions to the very real problem that exists as a result of the Northern Ireland Protocol.”
The Bill, which has already been through the Commons, cleared the Lords unamended without a vote and is now set to become law.