Bill Shorten has begun his tour of marginal seats by challenging Malcolm Turnbull to a formal debate about the goods and services tax, even though the Coalition is yet to finalise its election year tax policies.

The Labor leader proposed a showdown at the National Press Club, which he said should be held on the day before parliament resumes in February.

“I challenge Malcolm Turnbull to a debate about raising the GST to 15% and I will put the case against it and we’ll see if he’s willing to turn up and put the case for increasing the GST to 15%,” he said during a visit to the New South Wales seat of Eden-Monaro on Tuesday.

In proposing a debate, Shorten employed a tactic sometimes used by opposition leaders to put pressure on a rival. Prime ministers usually reject such requests and argue parliament provides a forum for debate.

It is not the first time Shorten has made such a request. In June last year, amid scrutiny of his leadership of the Australian Workers’ Union, Shorten challenged the then prime minister, Tony Abbott, to “make my day” by participating in a town hall-style debate on workplace relations.

Shorten’s visit to a Woolworths shopping centre in Queanbeyan on Tuesday indicated he intends to keep the political focus on the GST as the government considers options for the tax white paper due to be released this year. The government has said all options are on the table.

Shorten accused Turnbull of looking at increasing the GST while going soft on multinational corporations, meaning “everyday Australians face the prospect of paying a 15% price hike on everything”.

The wording is reminiscent of Abbott’s campaign against the former Labor government’s carbon pricing plans, which he described as a “giant new tax on everything”.

Shorten vowed to keep the GST pressure up until the election, which is due in the second half of the year but could be earlier if the government finds a viable double-dissolution trigger.

Turnbull is due to discuss health funding with state and territory counterparts at the next Council of Australian Governments (Coag) meeting in March. Premiers have aired their concerns about the impact of the $80bn cut from long-term projected hospital and school funding in Abbott’s first budget in 2014.

Shorten played down the suggestion of a split with state Labor counterparts such as the South Australian Labor premier, Jay Weatherill, who has been prepared to consider changes to the GST as part of a package to address the budget challenges.

Shorten said the federal government’s cuts had put state leaders “between a rock and a hard place” and he understood “why some premiers are saying what they are saying”.

“What I also understand is you don’t solve a problem by putting a new tax of 15% on everything,” he said.

Shorten, who was the preferred prime minister for only 14% of the electorate in the final Newspoll of 2015, has foreshadowed a three-week national tour of marginal seats focusing on GST, penalty rates and health. It is part of his attempt to erode the Coalition’s 53% to 47% lead in the two-party-preferred stakes.

The education minister, Simon Birmingham, said the leadership change from Abbott to Turnbull had delivered a “boost of optimism around Australia” but he expected the government to run full term. He criticised Shorten’s GST campaign.

“I think there is absolutely a case for us to have a look at tax reform in a complete way which is what the Turnbull government is doing by being mature and sensible, not ruling things in or out but looking at the entirety of the tax system to make sure it can grow our economy as effectively as possible,” Birmingham said.

“Mr Shorten is being grossly irresponsible by ruling out matters in relation to tax reform without giving that comprehensive and sensible look which we are undertaking through the tax reform white paper process.”

The government has signalled it will begin the parliamentary year by reintroducing legislation to revive the Australian building and construction commission and a tougher version of the registered organisations bill previously blocked by the Senate. The emphasis on workplace relations follows the publication of the final report of the trade union royal commission in late December.

Shorten acknowledged the commission “did discover some examples of bad behaviour within some parts of the union movement” and vowed to study the recommendations, but he did not believe in different rules for construction workers.

“I despise thievery, I despise people taking money from union members,” he said.