President Nicolas Sarkozy will be fighting for his political life when he makes a live appearance on French TV tonight. Some senior figures within his own party fear that he has already lost all chance of winning the two-round presidential election in April and May. There is speculation – possibly rooted in wishful thinking – that Mr Sarkozy may soon be tempted to throw in the towel and allow another senior centre-right politician to run in his place.

Sources within his centre-right party insist that the President will make no dramatic statements tonight. He will not say that he is pulling out of the race. Nor will he declare – yet – that he is a candidate for another five-year presidential term. His TV address to the nation will be purely presidential, they insist: announcing a programme of "urgent" and "revolutionary" reforms to make the struggling French economy more competitive. This will include a controversial plan to shift part of the high pay-roll tax burden on French employers to a higher rate of VAT.

But the tone and contents of Mr Sarkozy's address will be closely watched by supporters, and rivals, within his centre-right party, the Union pour un Mouvement Populaire (UMP). The President upset some of his supporters last week with off-the-record comments in which he said that he would give up politics if he lost the election.

This was interpreted by some politicians and commentators as a sign that Mr Sarkozy had become defeatist and had no stomach for the fight. The Socialist candidate François Hollande is comfortably ahead in the opinion polls and has given a series of eloquent and confident performances in campaign rallies and TV appearances in the past week.

President Sarkozy is said to have been "rattled" and "depressed" by the loss of France's triple-A credit rating earlier this month. Officially, he remains convinced that Mr Hollande's support will "melt away" in February. Unofficially, he is said to fear that his personal unpopularity and the French and European economic crises now make his re-election impossible.

Senior ministers have been at pains in recent days to quash the rumours that Mr Sarkozy, who turned 57 yesterday, might stand aside. "Is there any doubt about the candidacy of Nicolas Sarkozy? The answer is no," said the finance minister, François Baroin.

All the same, there is growing impatience, and alarm, within Mr Sarkozy's party at the tenacious popularity of Mr Hollande and the President's refusal to join the campaign. The President is said to believe that his best chance of winning is to remain "presidential" as long as possible. He wants to be seen, not as a candidate, but a statesman fighting for the future of France, and of Europe, at events such as the summit in Brussels on Tuesday which will discuss the new treaty on fiscal discipline within the eurozone.

Tonight's live TV address by Mr Sarkozy, and the promised "revolutionary" economic proposals, are, in truth, campaign events in all but name. But some nervous UMP politicians fear that Mr Hollande will be uncatchable if Mr Sarkozy does not formally join the race and exercise his redoubtable campaigning skills in the next few days.

UMP parliamentarians also fear that some of the President's remaining support could begin to drift to the far-right candidate Marine Le Pen or to the perennial centrist, François Bayrou. This would open up the possibility that President Sarkozy could suffer the humiliation of being eliminated in the first round, on 22 April, and fail to reach the two-candidate run-off on 6 May.

At present, Mr Hollande's first-round poll score is between 27to 30 per cent; Mr Sarkozy is on 22 to 23 per cent; Ms Le Pen between 18 and 21 per cent; and the centrist Mr Bayrou at 13 to 14 per cent.

In the second round, Mr Hollande is shown as defeating Mr Sarkozy by scores of between 40 and 60 per cent.

Lionnel Luca, an outspoken right-wing member of Mr Sarkozy's party, said that it would be "fatal" if the President waited, as rumoured, until the end of February or early March to enter the race. "Waiting another two months, taking more blows than we are giving, would be a political blunder," he said. "I hope [the President] will have the intelligence not to persist in this error."

There has also been talk among UMP deputies of the possibility that Mr Sarkozy might decide – or be politely asked by party leaders – to stand aside. Alternative candidates would include the Prime Minister, François Fillon, or the foreign minister, and former prime minister, Alain Juppé.

The Socialist candidate, Mr Hollande, raised this possibility in a live TV debate with Mr Juppé on Thursday night (which Mr Hollande comprehensively won). "Maybe, you will be the candidate," he said, teasingly. Mr Juppé did not react.

Both the UMP and Mr Hollande's Socialists are said to dread a new surge in support for the centrist Mr Bayrou. His somewhat vague, anti-establishment campaign is increasingly attractive to voters who cannot stomach either Mr Sarkozy or his Socialist challenger.

If Mr Bayrou was to sneak into the second round, he could be a serious threat – maybe the only remaining threat – to Mr Hollande's hopes of becoming president. This alone could produce a landslip of Sarkozy supporters to Mr Bayrou.

There was a surreal moment in Thursday's TV debate in which Mr Hollande appeared to become, briefly, a Sarkozy cheerleader. Asked if the President might pull out of the race, an alarmed-looking Mr Hollande said that he had great admiration for Mr Sarkozy's "tenacity" and "skills as a political warrior".