The prime minister and treasurer have had a tough day selling the federal budget to a wary electorate, including a sex worker and a social worker.

A casual wink, a sex worker, university protesters and his daughter have landed Prime Minister Tony Abbott in hot water.

Mr Abbott continued his post-budget pitch on Wednesday, taking to the airwaves in Melbourne after cancelling a visit to Deakin University over student protest security concerns.

Things began hotting up with a call from a 67-year-old grandmother, who works on an adult sex line.

Mr Abbott winked and smiled at host Jon Faine as Gloria told of surviving on $400 a fortnight and dealing with chronic illnesses.

“What do you suggest I cut out Mr Abbott? Food, electricity, firewood, Christmas and birthday presents to my grandchildren?” she asked.

“Or should we all just die and get out of your way?”

The prime minister, who is also minister for women, said he understood she was “doing it tough”, but believed axing the carbon tax would help her cost of living.

Australian Greens Senator Sarah Hanson-Young said the prime minister had not taken the woman’s concerns seriously.

“What a total creep,” she said.

Another caller, Stella, accused Mr Abbott of being “condescending” by not answering straight questions about the government’s broken election promises.

Mr Abbott also found himself on Fairfax radio trying to empathise with a social worker, Chantelle, who was worried she would lose her job when her three-year contract expired.

“Look, I have a three-year contract as well and I don’t know what’s going to happen after three years,” he said.

Treasurer Joe Hockey was also feeling the heat at an Australian Council of Social Service function in Sydney.

He snapped at photographers as he attempted to answer questions from welfare group leaders about the tightening of family payments, welfare and pensions.

“It’s just becoming really annoying,” he said of the press gaggle.

He was also surprised when a female member of the audience leapt up and put a business card in his lap.

“I was thinking I was going to need police protection there,” he joked.

Mr Abbott’s day was bookended by reports his daughter Frances received a scholarship from a design institute chaired by a friend and donor to her father.

His office said Frances had received the scholarship on merit and the PM was under no obligation to declare it on his pecuniary interest register.

Greens Senator Lee Rhiannon will be probing the issue further, as the institute’s chairman Les Taylor is listed on the NSW Electoral Funding Authority register as having donated more than $20,000 to the NSW Liberal Party.