The warning from well-known Brexit supporters comes after tens of thousands of people marched in central London, demanding a final vote on any United Kingdom exit deal.
"If we actually say we'll accept any deal you give us rather than walk away, that weakens our negotiating position", he told Sky's Ridge on Sunday.
Government sources told The Times that Mrs May is set to ask the European Union for another two years of transition - extending the period before full Brexit to seven years after the public voted for it.
However, Theresa May has also been urged by hardline Brexiteers to speed up preparations for a "no-deal" Brexit to put pressure on Brussels during withdrawal negotiations.
Addressing the crowds Sir Vince Cable said: "There are lots of things we didn't know at the time.More news: Virginia Restaurant Faces Backlash After Booting Out Sarah Sanders
The younger people in this country, many of whom will be out there marching today, are going to have to live with these decisions", he said.
Airbus alone employs almost 14,000 workers in the United Kingdom.
"Together we must stand up, demand our voices are heard, demand a people's vote", she said.
Companies including Airbus, BMW and Siemens have all sounded the alarm over the consequences of a 'no deal scenario.' While their comments refer to a worst case scenario (a complete breakdown of talks, no agreement on trade and no deal with the EU) their frustrations are entirely understandable.
The report said: 'This scenario would force Airbus to reconsider its investments in the United Kingdom, and its long-term footprint in the country'.More news: Uber Driver Was Reportedly Watching ‘The Voice’ On Hulu Before Fatal Crash
The rally was organized by the anti-Brexit campaign People's Vote, which is pushing for a public vote on any final divorce deal agreed with the EU. They don't want some sort of hopeless compromise, some perpetual pushme-pullyou arrangement in which we stay half-in and half-out in a political no man's land - with no more ministers round the table in Brussels and yet forced to obey European Union laws.
"They want this Government to fulfil the mandate of the people and deliver a full British Brexit".
An anti-Brexit, pro-EU supporter holds a placard during a protest across the street from the Houses of Parliament in London. Brexit is not inevitable.
Both the Conservatives and the main opposition Labour Party oppose holding another Brexit referendum, but the smaller, centrist Liberal Democrats support a new vote.
The government is giving Parliament a vote on the final deal, if one is reached, in the autumn - but it remains unclear what will happen if they reject it.More news: Italy to seize German NGO rescue ship carrying 226 migrants
The CER estimate of a 2.1% smaller economy than if the United Kingdom had voted to remain in the European Union is equivalent to a knock-on hit of £23 billion a year to the public finances, some £440 million a week. But real growth fell short of the model's projections starting immediately after the Brexit vote, suggesting a likely - though not inarguable - culprit for the lag.