The Abbott government has abandoned a planned $2bn tax on bank deposits and deferred a highly controversial and divisive decision on competition law as it seeks to shift the debate from its deepening internal divisions on to the economy.

But its “jobs and growth” slogan could again be challenged Wednesday, with economists predicting sluggish, and possibly negative, growth when the June quarter figures are released.

The government was facing a backbench revolt over the yet-to-be-legislated banks deposit tax – which the May budget calculated would reap $2bn over four years.

The treasurer, Joe Hockey, conceded the tax – which was originally announced by the former Labor government and was intended to raise a “financial stability fund” – had been a “work in progress” for the Coalition, but said it was now not necessary because the banks had agreed to higher capital reserves. He denied reports he had argued the government should go ahead with the tax as a revenue measure.

The second item on Tuesday’s cabinet agenda was another discussion of how the government should respond to the competition policy review, which Guardian Australia revealed included a slide presentation from small business minister Bruce Billson about the so-called “effects test”.

This “effects test” has deeply divided cabinet and pitted the biggest companies in the country against the small business “engine room” that the government courted with its “have a go” 2015 budget.

Despite Billson’s slide presentation on the effects test having been circulated to ministers ahead of the cabinet meeting, Abbott said: “I don’t think anyone should expect the effects test to be something that goes before Cabinet today.”

“There will be a discussion about the recommendations of the review, the [competition policy] review but not the effects test. That’s something that we are still considering,” he said.

Abbott had left most ministers, and big business lobbyists, with the impression that he backed Billson’s plan to implement the competition law changes as advocated by the small business lobby and some business groups.

But after an intensive lobbying campaign against the changes by big business and deep opposition from senior cabinet ministers, his comments on Tuesday were much more equivocal, emphasising all the things the government had already done for small business.

Billson was trying to convince ministers he could “appease” the powerful Business Council of Australia while still implementing the changes, to which he has given vehement public support.

But several of Billson’s cabinet colleagues – including Hockey, attorney general George Brandis, trade minister Andrew Robb, finance minister Mathias Cormann and communications minister Malcolm Turnbull – are understood to have opposed the move.

Major companies including Telstra, Bluescope and Qantas are understood to have joined the two big supermarkets, Coles and Woolworths, as well as the BCA in a major lobbying campaign to defeat it.

The announcement – mid-cabinet meeting – that the government was abandoning a tax that had not yet been legislated appeared to be designed to deflect attention from cabinet minister Peter Dutton’s comments Tuesday morning that Fairfax media was conducting “a bit of a jihad” against the government, and from deepening concerns within the Coalition about the government’s performance.

Asked about Dutton’s comments, Abbott said: “I’m not going to get into all this insider stuff. Naturally it fascinates the media but as soon as I start talking about it, you’ll say that the government was distracted from its purpose.”

The bank deposit levy was proposed by the previous Labor government just before the 2013 election. It would have imposed a 0.05% levy on every deposit of up to $250,000. It was scheduled to start on 1 January 2016.

Greens treasury spokesman Adam Bandt accused the government of caving in to the big banks and blowing another hole in government revenue.