The toppling of the Barnier government after just three months in office would present President Emmanuel Macron with an unenviable dilemma over how to go forwards and who to appoint in his place.
The National Assembly is due to debate two motions brought by the hard-left and far-right in a standoff with Barnier over the budget, which saw the premier force through the social security budget without a vote.
The far-right National Rally (RN) of three-time presidential candidate Marine Le Pen is expected to vote for the motion put forwards by the left, giving it enough numbers to pass.
Asked on French television if there was a chance his government could survive Wednesday's vote, Barnier replied: "I want this and it is possible. It depends on the MPs...
"I think it is possible that there is this reflex of responsibility where -- beyond political differences, divergences, the normal contradictions in a democracy -- we tell ourselves that there is a higher interest," he said.
But most analysts believe the government is doomed with the far-right teaming up with the left in an unholy alliance.
'Political fiction'
The turmoil follows snap elections called by Macron in the summer which aimed, without success, to halt the march of the far right, and left no party or faction in parliament with a majority.
Barnier took office with the far right under Le Pen holding a sword of Damocles over its head, with the ability to topple the administration.
No new elections can be called for a year after the previous legislative polls, narrowing Macron's options. Some have even suggested the president, who is on a state visit to Saudi Arabia, could resign.
But Macron rejected calls to resign to break the political impasse, saying such a scenario amounted to "political fiction".
"It doesn't make sense... it's frankly not up to scratch to say these things," Macron told reporters on the sidelines of the visit to Saudi Arabia.
"It so happens that if I am before you, it is because I was elected twice by the French people. I am extremely proud of this and I will honour this trust with all the energy that is mine until the last second to be useful to the country," added Macron, who is due to serve until 2027.
Several prominent opposition figures and even some voices closer to the presidential faction have suggestion resignation could be Macron's only viable option.
'Unbearable cynicism'
Macron also accused Le Pen's RN of "unbearable cynicism" in backing the motion which threatens to topple the government of Barnier.
"We must not scare people with these things, we have a strong economy," he added.
While most commentators predict that the left and far right will team up to bring down the government, Macron appeared to hold out some hope saying he could "not believe" that the no-confidence motion would we passed against the government.
Candidates for the hot seat as premier are few and far between, with loyalist Defence Minister Sebastien Lecornu and Macron's centrist ally Francois Bayrou possible contenders.
If the government falls, it would be the first successful no-confidence vote since a defeat for Georges Pompidou's government in 1962, when Charles de Gaulle was president.
The lifespan of Barnier's government would also be the shortest of any administration of France's Fifth Republic which began in 1958.
Some observers have suggested that Le Pen, 56, is playing a high-risk game and seeking to bring down Macron before his term ends by ousting Barnier.
Le Pen is embroiled in a high-profile embezzlement trial. If found guilty in March, she could be blocked from participating in France's next presidential election, scheduled for 2027.
She has insisted, however, that the party's hardline stance was entirely due to a budget that would make the French poorer.
By following the "catastrophic continuity of Emmanuel Macron" the prime minister "could only fail", she wrote on social media.
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