OTTAWA (Reuters) - Canadian Prime Minister Justin Trudeau shows every sign of trying to battle his way through the biggest crisis of his tenure even as opinion polls show he stands a real chance of losing power in an election this October.

Canada's Prime Minister Justin Trudeau speaks during a Liberal Climate Action Rally in Toronto, Ontario, Canada March 4, 2019. REUTERS/Mark Blinch

A second member of Trudeau’s Cabinet resigned on Monday, saying she had lost confidence in how the government had dealt with allegations that officials inappropriately pressured former Justice Minister Jody Wilson-Raybould last year to try to help construction company SNC-Lavalin Group Inc avoid a trial on charges of bribing Libyan officials.

Treasury Board President Jane Philpott was one of the most respected members of government and political observers described her departure as a major blow.

Trudeau, who came to power in November 2015 promising to do more for women, has now lost two high-profile female ministers and his principal personal secretary in less than a month as the crisis deepens.

A government official said while Trudeau was disappointed by Philpott’s resignation, he would not be changing tack.

“We will not lose sight of the big picture, we will not lose sight of the reasons that people elected us,” said the official, who requested anonymity given the sensitivity of the situation.

Trudeau told a Liberal rally on Monday night that he took Philpott’s concerns seriously while noting that “we are allowed to have disagreements and debate.”

NERVOUS LIBERAL LEGISLATORS

Some nervous Liberal legislators say Trudeau needs to make changes to his inner circle and complain about a lack of communication from top aides.

But a Liberal with close experience of working with the prime minister said a major shift in tactics was very unlikely.

“He will always double down when under pressure,” said the Liberal. “That’s his way.”

An Ipsos poll for Global News released on Tuesday showed the Conservatives would get 40 percent support from decided voters compared with just 31 percent for Trudeau, more than enough to ensure his defeat.

Penny Collenette, an adjunct professor at the University of Ottawa and former national director of the Liberal Party, said Trudeau needed to quickly give his version of events.

“Governments survive resignations from high-profile cabinet ministers ... it doesn’t have to be fatal at all. But we’re now into the fourth week and every day that goes by without this closing is a day lost for this government in an election year,” she said by phone.

Gerald Butts, who quit last month as Trudeau’s chief aide, is due to testify to the House of Commons justice committee about the allegations on Wednesday.

There are no immediate signs of an attempt to pressure Trudeau to leave, if only because it can take years to force out a Canadian leader who does not want to go.

The heads of political parties are elected by members at formal conventions and cannot be sacked after a snap vote by parliamentarians, as is the case in Britain and Australia.

In statements to domestic media, every one of the 33 remaining Cabinet members - including Finance Minister Bill Morneau and Foreign Minister Chrystia Freeland - issued statements backing Trudeau.

“Removing a leader just a few months before an election would be suicide,” said another Liberal.

Trudeau dismisses opposition calls for a public inquiry, noting that Canada’s independent ethics commissioner is looking into the allegations. The commissioner, though, can take months to wrap up a probe and there is no guarantee the results would be released before the vote in October.