"If the Lords were seen to be frustrating the will of the people to an extent, it might well be the case that they are signing their own death warrant," the minister said.
"You could be talking about the Lords disappearing in its current form. They've manage to avoid abolition now for quite a long time."
The Supreme Court hearing, which will be televised, begins on Monday.
In advance of the trial, Tory whips have been preparing a short Article 50 Act of Parliament.
They believe that the legislation will be "tight" enough to avoid Europhile MPs tabling scores of amendments which could delay the bill.
May has vowed to trigger Article 50 by March next year. Sources close to the Prime Minister last night said that she is still "confident" her timetable will not be delayed even if the Government loses next week's court case.
"Theresa has made clear that the people bringing this legal action over Article 50 must not be allowed to thwart the will of the people," an ally of May said. "She will take exactly the same approach in the Commons when she addresses MPs."
Theresa has made clear that the people bringing this legal action over Article 50 must not be allowed to thwart the will of the people.
Another source said: "However much Remainers want to campaign against Brexit, we are sure they won't go as far as voting down Article 50 in Parliament. The British people made their choice. Using the Commons to try and defy that would be a step too far and we are confident they won't try anything like that."
Iain Duncan Smith, the former work and pensions secretary and senior Leave campaigner, said that the Article 50 legislation has already been drafted and that MPs could face 24-hour sittings in Parliament to ensure that the bill is passed quickly.
He said: "It's a very narrow and tight bill, it's very difficult to amend. It will get through the Commons pretty quickly. We can be in and out of this very quickly and get on with triggering Article 50.
"You could have 24 hour sittings to get it through. There's no question in my mind she will invoke Article 50 by the end of March. I'm pretty optimistic.
"It's already drafted, everything will be cancelled until it gets through both houses."
What is Article 50?
• Article 50 of the Treaty of Lisbon gives any EU member the right to quit unilaterally, and outlines the procedure for doing so.
• There was no way to legally leave the EU before the Treaty was signed in 2007.
• Gives the leaving country two years to negotiate an exit deal.
• Once set in motion, it cannot be stopped except by unanimous consent of all member states.
• Any deal must be approved by a "qualified majority" of EU member states and can be vetoed by the European Parliament.
• In November 2016, the High Court ruled that the Government cannot trigger Article 50 without MPs voting on the matter first.