They've decided to focus efforts on passing legislation in Parliament which can head off that scenario.
The talks were called by Labour Party leader Jeremy Corbyn who had suggested being a caretaker Prime Minister if the government loses a vote of no confidence.
A vote of no confidence is still being considered as an option - but many opposition MPs say they couldn't accept Mr Corbyn as a caretaker PM.
It sets up a Parliamentary battle next month over Brexit, with the UK due to leave the European Union on October 31st.
UK correspondent Olly Barratt says Jeremy Corbyn has accepted his preferred plan doesn't yet have enough support.
In: 'It hasn't...
Out: ...regard.'
Dur: 49 seconds
http://www.fsnradionews.com/feeds/0827brexit-ob1.mp3
ALT:
UK correspondent Olly Barratt says Jeremy Corbyn has accepted his preferred plan doesn't yet have enough support.
In: 'That idea...
Out: ...oppose.'
Dur: 37 seconds
http://www.fsnradionews.com/feeds/0827brexit-ob2.mp3