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 lost.
Boris Johnson said he did not want an election, but progress with the EU would be “impossible” if MPs won.
To call an election under the Fixed-term Parliaments Act, Mr Johnson would need support from Labour as he requires the backing of two-thirds of the UK’s 650 MPs to trigger a poll.
Jeremy Corbyn has insisted he would be “delighted” to “take the fight to the Tories”, but BBC assistant political editor Norman Smith said the momentum inside Labour was increasingly against giving Mr Johnson that support.
“Why? Because they don’t trust him not to change the date of the election to after 31 October, after we have left the EU without a deal,” our correspondent added.
The PM’s spokesman said it was simply wrong to suggest that polling day could or would be changed. They insisted again that Mr Johnson did not want an election but MPs determined to block no deal were forcing him into that position.
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 a no-deal Brexit and they have submitted a motion for an emergency debate to the office of Commons Speaker John Bercow.
If Mr Bercow approves their application, the debate will be held later after Parliament returns from recess on Tuesday afternoon.
Their proposed 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 that despite the “aggressive operation” against them, he believed there were enough Tory MPs behind the bill for it to succeed.
He said it was “rank hypocrisy” of Downing Street to have threatened them with expulsion from the party and deselection given how many current ministers had previously 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.
