Ms Bradley, who was addressing a meeting of the British-Irish Parliamentary Assembly in London, said the people had already spoken.
He said: "I think it's understandable there are jitters on all sides of this debate and we need to hold our nerve".
"The fact is the people spoke".
However, during her address Mrs May said: "We would not accept a position in which the United Kingdom, having negotiated in good faith an agreement which prevents a hard Border in Northern Ireland, nonetheless finds itself locked into an alternative, inferior arrangement against our will".
"That's what's coming from people, not from me, but from people on the ground".
So she was at pains to make clear that she would not countenance a scenario in which the United Kingdom could remain "indefinitely" in either an extended transition or backstop.
With just over five months until Britain is scheduled to leave the European Union, talks have stalled over a disagreement on the so-called Northern Irish backstop, an insurance policy to ensure there will be no return to a hard border on the island of Ireland if a future trading relationship is not agreed in time.
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Speaking to Channel 4 News, the leading Brexiteer warned the United Kingdom would end up leaving the European Union under World Trade Organisation (WTO) rules regaining full independence from the Brussels bloc while the EU will get "the opposite of what they want".
Negotiations on Britain's departure from the European Union are stalled on several issues, but primarily an Irish "backstop" both sides agree is needed to avoid a hard border between the United Kingdom province of Northern Ireland and the Irish Republic, an EU state.
As well as the transition period, May will expect tough questions from MPs on the controversial "backstop" policy for preserving the frictionless Irish border no matter what the outcome of Brexit talks.
The prime minister maintains that she will not accept the EU's preferred backstop solution of Northern Ireland effectively remaining in the EU's customs union and single market after Brexit, as this would create new checks between Northern Ireland and the rest of UK.
Steve Baker, a leading member of the pro-Brexit European Research Group of MPs, has said as many as 80 of its members would vote against the prime minister's deal should she bring it before parliament.
"Now, we are looking at that". It is a suggestion that has been put forward by the EU.
"For example, a short extension to the implementation period would mean only one set of changes for businesses - at the point we move to the future relationship".
Currently, every European Union state switches to summertime on the last Sunday of March and then back to winter time on the last Sunday of October, but Brussels is proposing to end this practice.
She told MPs that a UK-wide customs union with the EU or an extension of the implementation period would be acceptable - but only if the United Kingdom "could not be kept in either arrangement indefinitely".