Kate Hoey said there was no point pushing for a "compromise" Brexit deal in order to meet the October 31 deadline because Parliament may not pass it anyway.
The Labour MP told talkRADIO’s Julia Hartley-Brewer the Prime Minister must find a deal that is “right for the future of the country”.
“We have to make sure that at the end of it, if we are leaving we leave properly and there’s no point in rushing things now and saying if we give this little bit more we might just get a deal,” she said.
“If the Prime Minister came back with a wonderful deal they [Parliament] would still find a way of voting against it because they don’t want us to leave and they want to make life as difficult as possible.”
The European Union’s chief negotiator Michel Barnier said reaching a Brexit agreement before Parliament was due to sit on Saturday was “still possible”.
“Reaching an agreement is still possible. Obviously any agreement must work for everyone, the whole of the United Kingdom and the whole of the European Union,” he said.
“Let me add also that it is high time to turn good intentions into a legal text.”
Conservative MP Tobias Ellwood told talkRADIO that should Boris Johnson secure an EU deal he would then face an uphill battle to convince a Parliament he no longer controls.
“Positions have been entrenched and nobody’s going to get their perfect outcome but 100 per cent of us will have to live with whatever we end up. So there has to be some form of compromise,” he said.
“If you don’t have the numbers the only way you can possibly get any legislation through, Brexit or otherwise, is by throwing the net wider across the aisle to the other side.”
Crossbench Lord Digby Jones told talkRADIO a no-deal Brexit would result in economic problems for a few years, but the nation would “get through it”.
“Any Brexiteer who tells you no deal would be fine is lying. It won’t be fine; it’ll be two or three years of needing a lot of hard work” he said.
“I believe if the country comes together and if we actually pull this together there will be economic problems for a period of time but the nation will get through it.”