Labour frontbencher Emily Thornberry has told the BBC "all options remain on the table", including a new referendum, if MPs vote down a Brexit deal.
She was asked about party leader Jeremy Corbyn's comment to a German newspaper that Brexit cannot be stopped.
Labour would prefer a general election, she said, but could campaign for "a People's Vote" if it were not possible.
Tory cabinet minister Damian Hinds said MPs must "consider the alternatives" if they vote down the deal.
The government has not yet agreed a withdrawal deal with the European Union, ahead of the UK's exit from the bloc next March.
While the UK government says it is 95% agreed - they have been unable to agree on the mechanism for ensuring that there will be no return to border checks between Northern Ireland and the Irish Republic, if a future trade deal is not ready in time.
On Friday, transport minister Jo Johnson, who voted to remain in the EU, quit the government saying he could not support the deal and called for another referendum.
Meanwhile Tory Brexiteer Steve Baker and Sammy Wilson, Brexit spokesman for the DUP - whose party's support Theresa May relies on for key Commons votes - have written a joint article in the Sunday Telegraph warning they are prepared to vote down any deal over proposals to manage the Irish border issue.
On Saturday, Jeremy Corbyn was quoted in Der Spiegel, having been asked if he would stop Brexit, as saying: "We can't stop it, the referendum took place."
Asked if Brexit could be stopped on BBC One's Andrew Marr Show, Ms Thornberry said the results of the referendum should be "abided by" but there had to be an "injection of democracy" in between that result and going any further. That should be a "meaningful vote" in Parliament, she said.
But she said Theresa May was only offering a choice between the UK "falling off a cliff" - with no deal agreed - or "get on this bridge to nowhere", by backing her deal. She said Labour would refuse to "play that sort of game" and, if the vote was lost, the party wanted a general election.
She added: "If we don't have a general election, which we think we should have, then yes of course all the options remain on the table and we would campaign for there to be a People's Vote but, you know, there are several stages before we get there."
The People's Vote campaign group organised the march in London in October which it said attracted about 700,000 people. The group wants a referendum on the final withdrawal deal.
Ms Thornberry said Mr Corbyn's comments had to be seen in context and he was explaining that: "We had a referendum, that we are democrats over and above everything else."
At the Labour Party conference in September, party members approved a motion that would keep all options - including a fresh referendum - on the table if MPs are deadlocked over Brexit. Mr Corbyn has said he would respect the result of the vote.
Labour's shadow Brexit secretary Sir Keir Starmer wrote in the Sunday Times: "There is no duty on MPs to surrender to a bad deal."
Instead, he said that MPs would be able to table motions, press amendments and trigger a no-confidence vote in order to prevent the UK leaving without a deal at all.
Sir Keir said: "I remain as convinced as ever that the consequences of no deal would be so severe that it cannot be allowed to happen."
But Education Secretary Damian Hinds told the BBC that people would have to consider a deal as a whole, stating: "They need to think about what the alternatives are as well.
"It is no good just not liking individual aspects. If you're going to take that view, you have got to have in mind a realistic, viable, deliverable alternative.
"I think people are going to be getting behind this deal and saying 'yeah, let's get on with it'."
He added: "It is not necessarily going to be something everybody is going to think is absolutely perfectly what they want.
"But that's the nature of these things, there are some trade-offs."