Many analysts say Kan is likely to survive the vote in parliament, expected on Thursday, but that he will still face big hurdles implementing policies, including an extra budget to pay for rebuilding after the March 11 earthquake and tsunami.
At least one analyst, though, suggested he faced increasingly long odds for staying in office.
And one ally of Ichiro Ozawa, the prime minister's main rival within his ruling Democratic Party of Japan (DPJ), said the rebels could have enough votes to adopt the motion, which would force Kan to resign or call a snap lower house election.
Kan has refused to rule out an election. But analysts say such holding a poll would be tough while part of the country is struggling to recover from the nuclear and natural disasters.
Critics within Kan's ruling DPJ want the premier to quit before the no-confidence vote. That could clear the way for a new leader who could form a "grand coalition" or at least better cooperation with the main opposition Liberal Democratic Party (LDP) to break a parliamentary logjam.
"I think at the moment we have enough votes and that it's more likely that the motion will pass," Kenko Matsuki, ally of DPJ power broker Ozawa, told Reuters.
"But we want to find a way until the very end for Mr. Kan to take the decisive step, to resign on his own, so that we can prevent that from happening."
OLIVE BRANCH
The Asahi newspaper said more than 50 backers of Ozawa, who has been charged over a funding scandal, planned to support the no-confidence motion. That would fall short of the more than 70 DPJ votes needed to secure passage of the motion in the 480-member lower house, where the Democrats have 305 seats.
But independent analyst Minoru Morita said the tide was running against the premier.
"The number of DPJ rebels is growing," he said.
Kan, who took office last year as Japan's fifth premier in as many years, is struggling to control the crisis at Tokyo Electric Power Co's Fukushima atomic plant, pay for rebuilding the northeast region devastated by the tsunami, and craft tax reforms to pay for rising social security costs.
The U.N.'s nuclear power agency, the IAEA, on Thursday criticized Japan's reaction to the crisis, saying officials underestimated the risk of tsunamis and needed to closely monitor public and workers' health.
On Wednesday, he reiterated he had no intention of stepping down.
"I consider it as my task and the task of my generation to overcome the current 'crisis in a crisis' triggered by the March 11 disaster ... and set the path for breaking out of stalled growth," he told the upper house.
"I want to carry out that task."
Kan met younger lawmakers from both the LDP and DPJ before a scheduled debate in parliament with his main opposition rival.
The premier held out an olive branch to his critics by suggesting a parliament session set to end on June 22 could be extended. He also said he would consider submitting a second extra budget for the current fiscal year.
The opposition and DPJ critics want the session extended in order to deal with a second extra budget to fund the next phase of rebuilding from the tsunami in what will be Japan's biggest reconstruction project since the early post-World War Two era.
The government also needs to get parliament to enact a bill enabling the issuance of more bonds to finance 44 percent of the $1 trillion budget for the fiscal year already begun in April.
Kan's cabinet is, in addition, trying to finalize this month proposals for social security and tax reforms -- including a likely doubling of the 5 percent sales tax in stages by 2015.
Moody's Investors Service said on Tuesday that Japan might not be able to avoid a downgrade of its sovereign debt rating even if it presented a strong reform plan, in part because of concerns over political feuding.