Bill Shorten has been lobbied by one of his frontbench MPs to reconsider the party's support for the mining tax.
Meanwhile, Coalition MPs have questioned the government's decision to cut the Seniors Supplement in the party room.
Earlier, WA Labor MP Alannah MacTiernan said the party needed to “translate the concept of aspiration directly to WA voters”.
The Opposition Leader told his caucus that the party had a discussion about its position on the mining tax before the WA Senate vote.
Mr Shorten told Ms MacTiernan that the decision would be deferred to the national policy processes, but said the party's political momentum had improved since the disastrous April Senate re-run. He did not, however, rule out the party changing its position.
Ms MacTiernan, who was elevated by Mr Shorten into the position of opposition parliamentary secretary for Western Australia in March, is not alone in arguing for the party to reverse course on one of its signature policies under the Rudd and Gillard governments.
But her comments are one of the clearest signals yet that the ALP could move on from the disastrous implementation of the tax on resources that has failed to bring in the billions of dollars in revenue originally expected.
During the meeting Mr Shorten also rallied his MPs, warning them the Liberals could get “nasty and personal” following the calamitous plunge in opinion polling since the federal budget.
He said budgets were rarely news for longer than a couple of days and the budget was a reflection on Prime Minister Tony Abbott's character.
He cautioned there was a long way to go until the next election but said “the values that underpin this budget can define them way beyond the next few months”.
“People see us again as a unified party providing a clear voice opposing this government,” Mr Shorten said.
“People expect us to be the opposition.”
In the Coalition party room meeting, two Queensland MPs raised concerns about the decision to abolish the Seniors Supplement, which helps seniors pay regular bills such as energy, rates, phone and car registration.
The MPs said they had received “blowback” about the decision in their electorates and that it would be a hard sell. Prime Minister Tony Abbott said he understood their concerns but said the policy was necessary to help improve the state of the budget.
Mr Abbott acknowledged the government faced “testing times” after the budget, but urged his troops to be “indefatigable, relentless, decent, sympathetic, compassionate but unapologetic”.
Mr Abbott said the public recognises the government needs to address the “mess” Labor left them and Coalition needed to demonstrate “warm hearts, clear heads and a strong spine”.