Right-winger Bennett, a key figure in Israel's settlement movement, last year ended 12 continuous years of rule by Benjamin Netanyahu, Israel's longest-serving premier.
To do so, the former tech tycoon brought together an unlikely grouping united by little other than their opposition to Netanyahu.
They included leftists and centrists, religious and hard-line Jewish nationalist parties -- and, for the first time in Israel's history, a party drawn from the country's Arab-Israeli minority.
But after more than 150 Palestinians were wounded in clashes with police over a flashpoint holy site in Jerusalem, the Raam party -- largely backed by Muslim Arab-Israelis -- said on Sunday evening that it was suspending its membership.
"If the government continues its steps against the people of Jerusalem... we will resign as a bloc," Raam said in a statement.
That would be a serious blow to a coalition that already, two weeks earlier, lost its one-seat majority of 61 in the 120-seat Knesset, Israel's parliament.
The departure of Member of the Knesset (MK) Idit Silman, in a dispute over the use of leavened bread products in hospitals during Passover, left the coalition with 60 seats -- the same as the opposition.
Raam's threat to withdraw its four MKs poses the most serious threat yet to the coalition.
'Testing the limits'
Emmanuel Navon, a political science professor at Tel Aviv University, said the question of the Al-Aqsa compound, a flashpoint religious site known to Jews as the Temple Mount, "is testing the limits" of the coalition.
On the one hand, the coalition's right-wing members are demanding a heavy-handed "law-and-order" approach to dealing with Palestinian demonstrators, especially after a series of deadly attacks inside Israel.
But on the other, the sight of Israeli police officers deploying and firing stun grenades in one of Islam's holiest sites during the holy month of Ramadan has sparked outrage among Raam MKs and across the Muslim world.
"This will be a huge headache (for Bennett) to manage," said Navon.
Despite the crisis however, Navon said the coalition was likely to survive.
"Mansour Abbas (Raam's leader) has no interest in leaving the coalition. He took a huge political risk in joining, and he needs time to show his voters that it was worth it," Navon said.
"He wants to prove to his constituency that by being pragmatic, he managed to improve their daily lives, unlike the other Arab-Israeli parties."
Navon added that neither Abbas, nor anyone else in the government, had anything to gain from early elections.
"Everyone in the coalition has an interest in not rocking the boat," he said.
If Raam were to leave, the coalition would find itself in a minority government, with just 56 seats.
That would force it to strike deals with opposition parties every time it wanted to pass legislation.
Yet to topple the government, the opposition would have to cobble together an even less likely administration, bringing Arab parties into a coalition with Netanyahu's 53-seat bloc of right-wing, orthodox and far-right Jewish parties.
Moreover, in 2014, Israel passed a law that means the opposition must be able to present a majority government of 61 seats in order to replace the incumbent.
"Even if Netanyahu manages to gather a majority to topple the government, that wouldn't mean that he could reach a majority to propose a new one," said political science professor Shmuel Sandler from Bar-Ilan University.
"Nor could he add Raam, because the religious nationalists would oppose it," he added.
Another election?
However, Sandler said the latest developments could raise the prospect of the opposition gathering enough votes to dissolve the Knesset and trigger new elections -- the fifth in three years.
The political challenge comes at a tense time, when the Jewish Passover festival coincides with the Muslim fasting month of Ramadan. The Knesset is in recess until May 5.
But one other move could flip Israeli politics on its head: Netanyahu retiring from politics.
Some coalition members have refused to join a Netanyahu-led administration because the veteran premier is on trial for corruption.
Were he to quit politics, it could open the way for a new alliance to be formed.
"That would make it possible to form a government tomorrow, without going to new elections," Sandler said.
Navon agreed. "The government would fall in five minutes," he said.
But analyst Dahlia Scheindlin warned there was little chance of such a scenario.
"Bibi (Benjamin Netanyahu) isn't known for being someone who rolls over," she said.
