* Letta faces rush to cut deficit, prepare 2014 budget
* Berlusconi allies defiant after parliamentary defeat
* Solid Berlusconi breakaway group would boost Letta
* Senate vote on Berlusconi's future on Friday
By Gavin Jones
ROME, Oct 3 (Reuters) - Fresh from surviving a political crisis, Prime Minister Enrico Letta must return rapidly to Italy's daunting economic problems but much depends on the fate of the man who tried to bring him down, Silvio Berlusconi.
If a split in Berlusconi's People of Freedom (PDL) party becomes permanent after this week's failed attempt to topple Letta, the centre-right could become less bellicose in demanding the tax cuts that split the coalition and strained public finances.
An early signal may come on Friday when a cross-party Senate panel is expected to recommend the media tycoon should lose his seat in parliament following an August conviction for tax fraud.
Letta's supporters hope this will lead to the centre-right camp playing a more cooperative role in what has been an unruly left-right coalition. "It will be a test for the right to prove whether they have truly modified their line towards the government and towards Italy or whether once again the real issue for them is the legal situation of Berlusconi," said centre-left parliamentary deputy Dario Nardella.
Problems put on ice by the government crisis are more pressing than ever. Economy Minister Fabrizio Saccomanni will present delayed emergency measures next week to try to rein in an overshooting budget deficit.
Then by Oct. 15 the government must unveil its 2014 budget aimed at stimulating a stagnant economy while still holding the budget deficit below the European Union's ceiling of 3 percent of output.
With the euro zone's most sluggish economy for more than a decade and youth unemployment of 40 percent, Italy is in desperate need of political cohesion to pass overdue reforms to its labour market, education and justice systems.
Berlusconi was forced into a humiliating U-turn on Wednesday when PDL rebels decided to back Letta in a Senate confidence vote, defying the man who has dominated the centre-right for two decades.
Yet it is still unclear if the rebels led by Berlusconi's former lieutenant Angelino Alfano will launch a separate party, how solid it would be or how much public support it would get.
Some of those questions might have been answered at a news conference planned by Alfano and the other PDL ministers on Thursday which was cancelled at the last moment after a migrant boat sank off Sicily, killing more than 100 people.
Berlusconi and his followers were licking their wounds on Thursday but the 77-year-old leader remains formally in charge of the party and his rallying calls for tax cuts and against the left still hold appeal for millions of Italians.
"Losing a battle does not mean losing the war," one of his closest allies Daniela Santanche said. "This is not the end of the Berlusconi era and it's not the start of a new era."
On Thursday, Italian government bonds had recovered most but not all of their losses caused by Berlusconi's attempts to sink Letta, but analysts warned instability was still a concern.
"We continue to think that snap elections are likely to be held in the first or second quarter of next year," Barclays Capital wrote in a note to clients.
Ratings agency Moody's also warned on Thursday that the persisting political instability was a threat to its Baa2 rating on Italy and said it expected Rome to fail to bring the budget deficit below the 3 percent ceiling this year.
The emergency deficit cutting package was the spark which set off the political crisis when the cabinet failed to agree on the measures at a meeting last Friday which was also intended to cancel a planned increase in sales tax.
The sales tax increase went ahead on Oct. 1, to the fury of Berlusconi, retailers and consumer groups.
If the increase remains in place it will benefit state finances by 1 billion euros ($1.4 billion) this year and 4 billion in 2014 but may further depress already falling consumer spending as the economy struggles to emerge from its longest post-war recession.
Addressing the Senate, Letta made no reference to cutting the sales tax or to a previous promise, made at the demand of the centre-right, to eliminate the second instalment of the housing tax IMU, due in December.
Saccomanni and Letta would prefer not to scrap the IMU payment, which would make it much easier to meet this year's deficit target. If they can quietly forget the promise on IMU with the consent of Alfano's PDL rebels, that would be a sign of much easier times ahead for Letta and the government.