Amid continuing mass protests, students on Wednesday blockaded roads in several cities a day after at least one million people joined marches and threatened to force Dominique de Villepin's conservative government to back down on the law.
Scrapping the law could be the last nail in the coffin for Villepin's premiership.
His authority is under heavy public pressure, the government has suffered sliding poll ratings, and his arch rival, Nicolas Sarkozy - interior minister and the main conservative rival for the 2007 presidential elections - is gaining political capital from Villepin's misfortune.
Union leaders held talks with conservative legislators after Chirac last week effectively took Villepin off the case and promised parliamentary amendments to soften the "easy hire, easy fire" law in the euro zone's second-largest economy.
Rene Valladon, the Force Ouvriere union chief, said France's 12 main unions wanted the three-day-old First Job Contract (CPE) law repealed by April 15.
Bernard Thibault, the CGT union leader, said after the meeting with the legislators: "I think they are going to do the rounds before deliberating on the political strategy to end the crisis."
Villepin's popularity has taken a
hit from the youth protests
"We said what we had to say on the CPE, now we're waiting for the only plausible response likely to end the conflict - repeal," he said.
Meawhile, students have called for new protests on Tuesday while unions meet to plot strategy. The April 15 deadline coincides with the start of France's Easter holidays and could reflect concerns the protests might fizzle out over that period.
Villepin, whose poll ratings have plumbed to new depths, championed the law as a way to cut youth unemployment of 22%. Critics say the law, which allows firms to lay off under-26s during a two-year period, will fuel job insecurity.
In a fresh swipe at Villepin, Sarkozy called for an end to the use of a fast-track parliamentary procedure employed to force through the law.
Sarkozy told a convention of his Union for a Popular Movement (UMP), that Parliament, often a rubber stamp for the government of the day, should have more powers and be a place for the dialogue and compromise that were vital for "the success of any reform".
Sarkozy, who fears the turmoil over the law could hurt his presidential chances, appeared to gain the upper hand over his rival after Chirac last week called in the ruling UMP to mediate in the dispute, sidelining Villepin.
In parliament, Villepin said enigmatically he would "draw the conclusions" of any decisions made on the law, fuelling speculation about his future.
"We said what we had to say on the CPE, now we're waiting for the only plausible response likely to end the conflict - repeal"
CGT union leader
Some deputies suggested Villepin, who last week mistakenly used the word "resignation" instead of "decision" when answering a question in parliament, could stand down.
Villepin allies said it was not in his nature to quit.Chirac's office issued a statement that students and schoolchildren should go back to their classes, but hundreds of students erected makeshift blockades on major routes into the western cities of Poitiers and Rennes.
Traffic jams up to several kilometres (miles) long built up. Six hundred protesters blocked deliveries at a groceries market in Nantes, also in the west.