A successful no-confidence vote would fell the government and kill the legislation, which is set to raise the retirement age by two years to 64.
Finance Minister Bruno Le Maire on Sunday called the votes "a moment of truth" for the government.
Senior officials from the conservative Les Republicains (LR) party have said they will not get behind the no-confidence motions.
Le Monde calculated that at least 26 LR lawmakers would need to back the motion for it to succeed.
Even if the motions flop, Macron's failure to find enough support in parliament to put his pension system overhaul to a vote has undermined his reformist agenda and weakened his leadership, observers say.