But peers also made clear that they will eventually back down and let an unamended bill become law in the first half of March.
And that will allow Mrs May to invoke Article 50 in good time to avoid overtly spoiling the EU's 60th birthday bash in Rome on March 25th, a party she has already said she will not attend.
The real problem with the debate was its focus on procedure, not substance.
Peers are doubtless right to call for closer parliamentary involvement.
They are also right to object to Mrs May's plan to present Parliament after her Brexit negotiations with what Lord Kerr of Kinlochard, a former diplomat often credited with writing Article 50, called Hobson's choice: a bad Brexit deal or, in his view worse, no deal at all.
In effect, Mrs May has now set the terms of Brexit as either hard or chaotic.
Yet once Article 50 is invoked, the argument over Brexit will instantly become substantive.
Trading arrangements, a new migration regime, the future of regulation, security and defence co-operation, money and much else will be on the table.
And as Lord Hill, a former European commissioner, noted in the debate, what will matter then is not what the British government wants but what the other 27 countries are prepared to offer, as the bargaining power is mainly on their side.
The big risk is that the eventual result will be good neither for Britain nor for the EU.
In a new paper for the Centre for European Reform, a think-tank, Charles Grant notes that this is because “both the UK and the 27 are placing politics and principles ahead of economically optimal outcomes.”
Sadly, it was ever thus.