The PM faces a showdown in Parliament later as MPs aim to take control of the agenda to stop a no-deal Brexit.
Ex-chancellor and Tory rebel Philip Hammond said he thought there was enough support for the bill, seeking to delay the UK’s exit date, to pass.
No 10 officials warned the prime minister would push for an election on 14 October if the government loses.
Boris Johnson said he did not want an election, but progress with the EU would be “impossible” if MPs won.
Meanwhile, Jeremy Corbyn said the Labour Party was ready for a general election and would be “delighted” to “take the fight to the Tories”.
To call an election under the Fixed-term Parliaments Act, Mr Johnson would need support from Labour as he needs the backing of two-thirds of the UK’s 650 MPs to trigger a poll.
However, shadow Northern Ireland secretary Tony Lloyd later said Labour would vote against any government plans to hold a general election before the UK is due to leave the EU on 31 October.
He said Labour would not “fall for Boris Johnson’s trick” by agreeing to a general election before 31 October which could ultimately see the Tories gain a mandate for no deal.
Opponents of no deal believe it would harm the economy, cause severe disruption to travel and supplies of goods like food and medicine, and lead to a hard border on the island of Ireland.
Proponents insist, though, that any disruption would be short-lived and could be managed with careful preparation.
Mr Johnson has vowed to leave on 31 October with or without a deal.
A number of MPs against no deal have come together across party political lines to try to stop it, and when Parliament returns on Tuesday afternoon after recess, they are expected to put forward legislation under Standing Order 24 – a rule that allows urgent debates to be heard.
The bill would force the prime minister to ask for Brexit to be delayed until 31 January, unless MPs had approved a new deal, or voted in favour of a no-deal exit, by 19 October.
Mr Hammond told BBC Radio 4’s Today it was “rank hypocrisy” of Downing Street to have threatened Tory MPs with expulsion from the party and deselection if the back the bill given how many ministers had defied Theresa May over Brexit.
The former chancellor was reselected by his local Conservative Party Association on Monday to stand as its candidate in the next election and said Number 10 would have “the fight of a lifetime” on their hands if they tried to override that.
“This is my party. I have been a member of my party for 45 years, I am going to defend my party against incomers, entryists, who are trying to turn it from a broad church into a narrow faction,” he added.
Foreign Secretary Dominic Raab said the anti-no-deal bill “would create paralysing uncertainty”.
“It’s craftily designed to allow serial extensions, it would immediately require the UK to accept any EU conditions, however punitive, however harsh, and regardless of those conditions the price tag for the taxpayer would be £1bn each month,” he told BBC Radio 4’s Today programme.
“That is clearly designed to delay if not to cancel Brexit, and I think it scuppers the very positive progress we’ve had with the EU to get a deal.”
In a televised announcement on Monday, Mr Johnson insisted he could achieve changes to the current Brexit deal at an EU summit on 17 October, but taking no deal off the table would “plainly chop the legs out from under the UK position”.