Reviewing universal services such as free prescriptions and ending the council tax freeze in Scotland would "redistribute" money from the rich to the poor, according to Labour's chief whip.
James Kelly said the universal services that Labour once supported "have served Scotland well", but cuts to jobs and services mean the party's leaders must now "face up to our responsibilities".
When asked if Labour would introduce means testing, he said it would "look at all the options".
Pressed on whether Scotland's largest Labour-controlled council would go back on its manifesto pledge to freeze the council tax for five years, he said councils "need some flexibility around their fundraising options".
"We will not shirk from a situation where people on six-figure salaries are taking benefits from the system, and we will not shirk from redistributing that to those who need it most," said Mr Kelly.
Mr Kelly was asked four times if they would consider means testing on BBC Radio Scotland's Good Morning Scotland programme.
He replied: "We will look at all options, including simplifying the system. These policies have all served Scotland well, but we are facing a situation on the ground where 14,500 council workers lost their jobs last year.
"When people are losing their jobs we have a duty as a party, and we have a duty as MSPs, to look at another way of doing it."
He added: "The SNP are sticking their heads in the sand. We will face up to our responsibilities and we won't run away from redistributing areas of the budget to the poor and vulnerable that need it."
Writing on Twitter, Deputy First Minister Nicola Sturgeon said: "Quite disgraceful from Labour - attacking benefits that thousands rely on but refusing to be straight about their own plans. If the council tax freeze is so bad why, just five months ago, did they promise to continue it for five years?"