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 faces the prospect of losing power in an election this October.

A second member of Mr Trudeau’s Cabinet resigned on Monday, saying she had lost confidence in how the government had dealt with a scandal over whether or not officials had pressured the former justice minister to help a major company avoid being tried for corruption.

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

A government official said on Tuesday that while Mr Trudeau was disappointed by her 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.

Mr Trudeau told a rally of his Liberal Party on Monday night that he took Ms Philpott’s concerns seriously while noting that “in a democracy like ours ... we are allowed to have disagreements and debate”.

Some nervous Liberal legislators say Mr Trudeau needs to make changes to his inner circle and complain about a lack of communication from top aides as to how the prime minister plans to deal with the crisis.

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 the Toronto-based Global News released on Tuesday showed the Conservatives would get 40 per cent support from decided voters compared with just 31 per cent for Mr Trudeau, more than enough to ensure his defeat.

The official opposition Conservatives are demanding that Mr Trudeau step down, but the Liberals say it will be hard for other parties to keep the issue alive all the way until October.

There are no immediate signs of an attempt to pressure Mr 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.

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 Mr Trudeau.

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

Mr 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 an investigation and there is no guarantee the results would be released before the election in October. – Reuters