The Prime Minister could face difficulty activating Britain's exit from the EU as an increasing number of MPs have indicated they would vote against triggering Article 50 in parliament.
The government is appealing a High Court ruling that the PM must seek MPs' approval before the formal two-year process can be started.
But if the Commons vote goes ahead, a number of MPs have indicated they would oppose the measure unless there are major concessions.
Liberal Democrat leader Tim Farron said his party would vote against Article 50 unless there was a guarantee that the final Brexit deal with the European Union is put to a fresh referendum.
He said he respected the decision of voters in favour of leaving the EU but said that nobody should have the deal "imposed" on them.
Although his party only has eight MPs in the Commons, there are 100 Liberal Democrat peers which could spell trouble for the government as the legislation would have to clear both Houses.
He told BBC Radio 4's Today programme: "We believe that what started with democracy last June - which we totally respect - must not now end up with a stitch-up, with a deal being imposed on the British people that absolutely nobody voted for."
Farron's pledge comes after Labour leader Jeremy Corbyn said that the party will only let Theresa May trigger Article 50 if she guarantees access to the single market.
But in an apparent u-turn a day later, deputy party leader Tom Watson said Labour would support Theresa May in an Article 50 vote.
However Labour MPs, including a front-bencher, have indicated their intention to defy a Labour whip.
Labour's Shadow Foreign Office minister, Catherine West wrote on Twitter that she would respect the wishes of her constituents and vote against Brexit.
Labour MP, Helen Hayes, also said she would vote against Article 50.
She told Radio 4's Today: "I had somebody in my surgery last week who was in tears because of Brexit and I see genuine distress amongst my constituents about what this path means.
"I would not be representing them if I voted to trigger Article 50 on the basis of no information from the government about the path that they would then take us on."
Former Labour leadership candidate Owen Smith, ex minister David Lammy, and shadow minister Daniel Zeichner have also said they will vote against Article 50.
Brexit Minister David Jones said: "Parliament voted by a margin of six to one to put the decision on whether to remain in, or leave, the EU in the hands of the British people.
"Now, because they didn't like the first answer, Liberal Democrat and Labour MPs seek to put the question all over again in hope of a different answer.
"They are attempting to thwart and reverse the decision that was taken on June 23.
"Only the Conservatives can be trusted to respect the outcome of the referendum and make a success of Brexit."
In December, the government will challenge the Supreme Court ruling arguing that prerogative powers could be used to trigger Article 50.