Opening debate on the flagship EU Withdrawal Bill in the House of Commons, Mr Davis warned that the "cumulative effect" of a series of Lords amendments would "make it impossible to deliver the smooth and orderly exit we want".
Remain-supporting Conservative MPs had threatened to defeat the government on an amendment to the bill which would have given Parliament a wide-ranging veto to May's Brexit deal, or even force a second referendum.
The frontpages of Leave-backing British newspapers said accepting the amendments would betray the 52% who backed Brexit in the seismic 2016 referendum.
Brexit campaigners still expressed concern that the concession may open the door to the European Union trying to force Britain into retaining the closest possible ties with the bloc by weakening the government's hand in the talks.
"I am trying to negotiate the best deal for Britain".
Asked on BBC Radio 4's Today programme what would happen under Government plans if MPs voted against the deal eventually secured by Mrs May, Mr Davis said: "If they throw it out, well, they throw it out".
"I am confident I can get a deal that allows us to strike our own trade deals while having a border with the European Union which is as frictionless as possible".
After the resignation of justice minister Phillip Lee, who said he could not support the government's position on Brexit, it was said government whips feared a Tory rebellion on the "meaningful vote" amendment passed by the House of Lords.
"But if the Lords amendments are allowed to stand, that negotiating position will be undermined".
Several pro-EU Conservative MPs said they would join the opposition in voting against the government.
Brexit protesters outside Parliament House. The Daily Express featured the British flag as its front page with the headline: "Ignore the will of the people at your peril".
Britain's highest-selling tabloid, The Sun, which is owned by Rupert Murdoch, addressed lawmakers directly on its front page, saying they faced a choice between "Great Britain or Great Betrayal". May's preferred approach is temporarily keeping the U.K.in some form of temporary customs union with the E.U., but this is unacceptable to hardline Brexiteers in her party.
Shadow Brexit Secretary Keir Starmer commented: "This vote was about ensuring parliament was given a proper role in the Brexit negotiations and that we avoid a no deal situation, which is becoming more likely with the divisions at the heart of this government".