Johnson's Conservative government wants to pass an EU withdrawal agreement bill by Thursday. It has tabled a separate motion on the timetable for the 100-page bill.
Opposition lawmakers said parliament normally takes at least 10 days to scrutinize similar bills, claiming they are being asked to back a "blind Brexit."
"Ministers are trying to bounce MPs into signing off a bill that could cause huge damage to our country," tweeted Keir Starmer, Labour's Brexit spokesman.
Green Party lawmaker Caroline Lucas tweeted that parliament had "more time to debate the Wild Animals in Circuses Act (affecting 19 animals) than they will to decide the future of 65 million people."
But Steve Baker, the chair of the Conservatives' influential European Research Group (ERG) of eurosceptics, said much of the bill should be "intimately familiar" to lawmakers who scrutinised and earlier EU (Withdrawal) Act.
"The allocated time is sufficient," Baker tweeted.
Some analysts speculated that Johnson could scrap the whole withdrawal agreement bill if he loses a vote on the accompanying "programme motion" for its timetable.
"A vote against the programme motion is a vote against Brexit," tweeted Conservative eurosceptic Jacob Rees-Mogg, Johnson's leader in the Commons.
The bill, which could be amended in a longer parliamentary session on Wednesday, is designed to make Johnson's withdrawal agreement, which has the status of a draft international treaty, into British law.
It covers most of the crucial legal, financial and bureaucratic details of Britain's "divorce" from the EU.
Amendments have been tabled for Wednesday on keeping Britain in the EU customs union, holding a second Brexit referendum, and extending a 14-month Brexit transition.
Brexit Secretary Steve Barclay tweeted that the bill "delivers Brexit" by October 31.
The government decided to plough on with its legislative programme despite being blocked by the Commons speaker from from holding a vote on its Brexit deal on Monday.
Johnson had attempted to ignore the furore over his reluctant sending of an unsigned request to Brussels to delay Brexit late Saturday, accompanied by a signed letter explaining that he does not want a delay.
The remaining 27 EU capitals are closely watching events in London and will decide in the next few days how to respond to Johnson's request, European Council President Donald Tusk said Tuesday.
"It is obvious that the result of these consultations will very much depend on what the British parliament decides, or doesn't decide," Tusk told the European Parliament during its plenary session in the French city of Strasbourg.
"A no-deal Brexit will never be our decision," he stressed, implying that the EU would rather agree to an extension than see Britain leave without a deal in place.
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