Sharon has said the alternative Middle East plan is "more dangerous" than the now-defunct Oslo peace accords, insisting that the internationally-backed "roadmap" is the only path to peace, even though it has made scant progress since its launch in June.
According to Joseph Alpher, an advisor to former prime minister Ehud Barak during the Camp David peace talks in July 2000, Geneva serves as a challenge to Sharon to come up with his own solution.
"He (Sharon) would define Geneva as a red warning light that he better look after the public ... and embark on his own counter-offensive," said Alpher.
"He wants the public to feel once again he can deliver on peace ... and wants the Americans to believe that as well."
The Israeli promoters of the initiative have said they were taken aback by the force of Sharon's denunciation, but with everyone from Palestinian leader Yasser Arafat to US Secretary of State Colin Powell voicing praise for the instigators' efforts if not the end result, Sharon may have felt he had little option.
In a recent interview in which he mused over the idea of launching unspecified "unilateral" gestures towards the Palestinians, Sharon said he "just wanted the Israeli public to know that its prime minister has not stopped thinking how to get out of the impasse."
The chief driving force on the Israeli side, ex-minister Yossi Beilin, feels the initiative has already had an impact, pointing to signs of a recent softening of Sharon's hard line, such as an order to ease restrictions in the Palestinian territories.
But Dan Schueftan, of Haifa University, said Beilin was indulging in wishful thinking if he thought his project had put Sharon on the defensive.
"That's exactly what Yossi Beilin and the Europeans want to think," he said.
Schueftan said Sharon was well aware that he was being criticised by the Israeli public and Washington "for not initiating anything and not trying hard enough".
But by opting for unilateral measures, Sharon was rejecting the principle behind Geneva that a Palestinian partner could be found, said Schueftan.
Bush recently criticised the "humiliations" heaped on Palestinians by Israeli forces and a separation barrier being built in the West Bank for prejudicing the boundaries of a future two-state settlement.
Sharon was also rattled by army chief General Moshe Yaalon, who said the restrictions on Palestinian civilians could lead to a greater eruption of violence while four former heads of the Shin Beth interior security services warned of the "disastrous" consequences of continued occupation.
Aharon Klieman, a professor at Tel Aviv University, said Sharon was much more concerned by "criticism within government and the military that the situation is barely containable as indeed the Americans have also argued for some time", than anything the Geneva backers had to say.
"He (Sharon) holds Geneva in disdain and is not moved by the initiative," Klieman added.
Sharon diplomatic advisor Zalman Shoval also denied the premier had been stung into action by Geneva.
"The so-called Geneva initiative has very, very little support in Israel," Shoval told AFP. "The public have no trust in the people behind it... There's much more interest abroad than here."
But Alpher said that just by showing some kind of agreement is possible, Geneva inevitably obliged Sharon to respond in kind.
"It's what obliges him to say that 'I have a plan which works, that has two feet on the ground and that's responsible'," said Alpher.
"This is the challenge: can you come up with a plan that can reassure Israelis about their security and the long-term Jewish and democratic nature of their state in the way that Beilin has?"