"Of course it is an ultimatum. The government and the president have effectively 48 hours to decide," Rene Valadon from the Workers' Force (FO) union said.
Police arrested over 160 people on Saturday on what had been a mainly peaceful day of protests.
Trades unions claim the new law will allow employers to exploit young people who work for them but the government says it will help cut youth unemployment by making the labour market more flexible.
Unions said 1.5 million protesters took part in more than 150 rallies across France against the government's First Employment Contract (CPE) on Saturday but the interior ministry estimated the overall turnout at just over 500,000.
Government spokesman Jean-Francois Cope said on Saturday night that the government wanted dialogue, but gave no signs that it was going to withdraw the law.
Student and union leaders have been asking President Jacques Chirac not to sign the law, which he must do for it to take effect as expected in April.
Demonstrators are totally opposed to the new law, which will let employers terminate job contracts for workers aged under-26 at any time during a two-year trial period without having to offer a reason or give any warning.
