WA Labor's senator-elect Joe Bullock has again rejected a union's call for his resignation, saying he wants to work to regain the trust of workers.

Despite supporting his preselection, the United Voice union yesterday launched a public attack on Mr Bullock, criticising a speech he made last year where he described some Labor members as "mad".

Today Mr Bullock told ABC Local Radio he would not resign because he wanted to help Labor win back the trust of working people.

"I believe in order to be successful, the Labor Party needs to reconnect with workers and their families in this state and I think that the Labor Party would benefit from being reminded of that," he said.

"I want to ensure the focus of Labor remains, as it has been for 100 years, on improving the lot of working people. That's what I've been doing for the past 37 years.

"I believe at this stage of the Labor Party's history, when things are not going all that well for them in many respects, that it's time to refocus on our core business, which is standing up for and standing by, improving the living standards of working people, not allowing the Abbott Government to undermine them.

"The future success of the Labor Party is about winning back that trust, and the Labor Party has to consistently demonstrate that it's worthy of it."

The party's vote collapsed to less than 22 per cent in last Saturday's Senate election re-run in WA, leaving Senator Louise Pratt fighting for her political life against Liberal Linda Reynolds.

Yesterday United Voice WA branch secretary Carolyn Smith said Mr Bullock was unfit to lead the party and should quit.

"If we had had the information we have now, if we'd known the comments and his views on party members, if we'd known the sort of comments he'd made about Louise Pratt, we would not have supported him," she said.

Mr Bullock had been placed first on Labor's ticket due to a factional deal brokered by United Voice and the right.

When asked about the union's call to stand down today, he said Ms Smith had "succumbed to pressure from her friends in her section of the party".

Bullock concedes he voted against Labor

In last year's speech, Mr Bullock admitted he had not always voted Labor, but after reports of his comments surfaced this month, he stated that was before he joined the party in 1978.

But today Mr Bullock said he had not always voted for Labor in the Upper House, even after joining the party.

"There have been times when I've got two votes for the price of one, not by voting twice, but rather by in the Upper House giving the Australian Christians my first vote, and then voting for the Labor Party," he said.

"That records support for the Australian Christians, but still delivers a vote for the Labor Party."