At least one MP, Jean-Michel Clement, is planning to vote against the law — at a cost of being kicked out of Macron's En Marche (Republic On The Move) party — while several others said they would abstain.
The lower-house national assembly was supposed to vote on the bill Friday, but the fractious debate stretched into the weekend due to more than 1,000 amendments proposed by MPs.
More than 200 of the changes were suggested by En Marche members as Macron's own MPs openly challenged his plans to double the maximum time migrants can be held in detention to 90 days.
The government defends the bill as balanced, but it has attracted criticism both from rightwingers who say it is too soft and leftwingers who have blasted it as repressive.
Interior Minister Gerard Collomb said it aims for “better controlled” immigration, halving the waiting time for asylum applications to six months while also making it easier to deport those turned down as “economic”
Accepted refugees will be given more help to integrate, such as better access to work and French lessons.
Many left-wing opponents lashed out in parliament at measures to keep asylum seekers awaiting deportation, including children, in detention for up to 90 days.
“Nothing justifies locking up a kid,” said Socialist MP Herve Saulignac.
The bill also reduces the time that asylum-claimers have to lodge their application from 120 to 90 days and gives them two weeks to appeal if unsuccessful, which NGOs say is not enough to gather more evidence in support of their claim.
Despite rumblings of revolt, the bill is expected to pass, with En Marche holding more than half the seats after battering traditional parties in June's parliamentary elections.
France received a record 100,000 asylum applications last year, bucking the general trend in Europe where the number of asylum seekers halved between 2016 and 2017.
Many Africans and South Asians end up sleeping on the streets of Paris due to a shortage of accommodation, or camping out in Calais hoping to stow away on trucks to Britain.
Pressure over the immigration bill comes as Macron insists he will push on with sweeping reforms including an overhaul of state rail operator SNCF, despite strikes and street protests.
Monday sees the start of another two days of strikes by rail workers over the shake-up which have been causing havoc for French commuters two days out of five since the start of April.
Rail unions object to plans to strip new SNCF recruits of jobs-for-life and early retirement, part of Macron's bid to reduce the SNCF's nearly 50 billion euros of debt.
The unions are gambling on public opinion turning in their favour but polls suggest an opposite trend, with just 43 percent backing the strike in an Ifop poll released Sunday.
The scale of the disruption has also eased over the course of the month as fewer workers continue with the strike.
On Monday, 35 percent of high-speed trains are set to operate — up from just an eighth at the beginning of the month.