* League leader wants Senate debate to unseat government
* Senate chiefs fail to agree date for no-confidence vote
* 5-Star says Italians will make Salvini pay for crisis (Recasts after Senate called back to decide date for debate)
By Gavin Jones and Crispian Balmer
ROME, Aug 12 (Reuters) - Right-wing League leader Matteo Salvini's drive for early elections in Italy hit a road bump on Monday with parliamentary party leaders failing to decide when the Senate should debate his no-confidence motion in the government.
The deeply divided parliamentary chiefs ordered the full upper house Senate to break its summer recess on Tuesday to decide for itself on when to hold the vote, which looks set to trigger the downfall of Prime Minister Giuseppe Conte.
Salvini, now interior minister in a year-old coalition with the anti-establishment 5-Star Movement, wants to capitalise on his surging popularity in the opinion polls and hold a new election that could see him crowned as prime minister.
But the 5-Star and many lawmakers from the opposition centre-left Democratic Party (PD) are furious over Salvini's manoeuvring and want to slow his charge to the ballot box, saying this will torpedo key bills and damage Italy's fragile finances.
"You will see that Italians will make the League pay for the stab in the back it has dealt Italy," 5-Star leader Luigi Di Maio said on Facebook.
Di Maio ruled out rumours that he might hook up with former PD Prime Minister Matteo Renzi to form an alternative coalition. But looking to play for time, both the 5-Star and PD said Conte should address parliament on Aug. 20 over the crisis and not Aug. 14, as the League has demanded.
The Senate will set the calendar for the unprecedented summer political crisis at a session due to start at 6 p.m. (1700 GMT) on Tuesday.
Italy's parliament is normally closed for most of August and the country has not held a national election in the autumn for a century because it is the time the government traditionally uses to draw up the budget - an elaborate, time-consuming process.
Ahead of the Senate session, Salvini is expected to meet former centre-right prime minister Silvio Berlusconi, who leads Forza Italia (Go Italy), to discuss reviving a long-standing electoral pact between their two parties.
The anti-EU Salvini said this year that he wanted to break free from the pro-European Berlusconi. However, Forza Italia politicians could try to use their numbers in parliament to block any rush to early elections if Salvini spurns them.
Salvini, photographed at the weekend posing for shirtless selfies with supporters at the beach, has dominated Italian politics since forming a government with 5-Star. He has campaigned non-stop, promoting a "man-of the people" image and touting a popular clampdown on illegal immigration.
However, some League voters have been dismayed by his decision to sink the government and have voiced dissent on social media. Salvini was booed and heckled during campaign stops in Sicily on Sunday.
His move to ditch the coalition also raised the government's cost of borrowing and sparked a sell-off in shares.
On Monday the spread between Italian benchmark bonds and safer German Bunds stood at 230 basis points, some 30 points higher than where it had stood before Salvini's surprise decision on Thursday. (Additional reporting by Reuters TV and Isla Binnie Editing by Mark Heinrich)